Mathematics High School

trigonometric ratios

Answers

Answer 1

Answer:

[tex]\boxed {\boxed {\sf x \approx 41}}}[/tex]

Step-by-step explanation:

Remember the three trigonometric ratios:

sinθ= opposite/hypotenusecosθ=adjacent/hypotenuse tanθ=opposite/adjacent

Examine the triangle. We have an angle measuring 59°.

The side measuring 35 is opposite the angle. x is the hypotenuse because it is the longest side.

Since we have the opposite side and the hypotenuse, we use sine.

[tex]sin \theta= \frac {opposite}{hypotenuse}[/tex]

[tex]sin 59=\frac{35}{x}[/tex]

Now, solve for x by isolating the variable. We can cross multiply. Multiply the first numerator by the second denominator. Then, multiply the first denominator by the second numerator.

[tex]\frac {sin59}{1}=\frac{35}{x}[/tex]

[tex]sin59*x=35*1 \\[/tex]

[tex]sin59*x=35[/tex]

x is being multiplied by sin 59. The inverse of multiplication is division. Divide both sides by sin59.

[tex]\frac {sin59*x}{sin59}=\frac {35}{sin59}[/tex]

[tex]x= \frac {35}{0.8571673007} \\[/tex]

[tex]x=40.8321689[/tex]

Let's round to the nearest whole number.

40.8321689

The 8 in the tenths place tells us to the 0 to a 1.

[tex]x \approx 41[/tex]

The hypotenuse of the triangle is approximately 41.

Answer 2

Answer:

[tex]\displaystyle 41 \approx x[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{x}{35} = csc\:59 \hookrightarrow 35csc\:59 = x; 40,832168903... = x \\ \\ \boxed{41 \approx x}[/tex]

[tex]\displaystyle \frac{35}{x} = sin\:59 \hookrightarrow xsin\:59 = 35 \hookrightarrow \frac{35}{sin\:59} = x; 40,832168903... = x \\ \\ \boxed{41 \approx x}[/tex]

Information on trigonometric ratios

[tex]\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOCITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:θ \\ \frac{ADJACENT}{OPPOCITE} = cot\:θ[/tex]

I am joyous to assist you at any time.

Related Questions

I need help it’s really easy I just wasn’t paying attention

Answers

Answer:

simple how many 1/2 are in 4 the answer would be 8 y=8 can i have brainliest

Step-by-step explanation:

Answer: 30/6=5 100/4=25

Step-by-step explanation:

i am 7 digit number my digit are fromed as the skip count of 3 by 4 times find the place value of my middle digit

Answers

Answer:

7 is in thousands place and its place value is 7000, 2 is in hundreds place and its place value is 200, 6 is in ten place and its place value is 60, 3 is in ones place and its place value is 3.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The place value of a 3-digit number helps in understanding the value of each of the digits. The smallest of 3-digit numbers is 100 and the largest number is 999.

Step-by-step explanation:

HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP

Answers

Answer:

Parallelogram

Step-by-step explanation:

Compare the weight of the puppy and the dog using percentages.

Answers

Answer:

what are their weights

Step-by-step explanation:

In ΔRST, s = 7.3 inches, t = 3.1 inches and ∠R=138°. Find the area of ΔRST, to the nearest 10th of a square inch.
big test, half grade, last problem, please lord

Answers

Answer:

5.1 inches

Step-by-step explanation:

Five triangles make up the pentagon.

The area of each is aside

The area of the pentagon is 5

Substitute values and calculate

Which equation represents the line that passes through the
point (9.4) and is perpendicular to the graph of 5x + y = 30

Answers

Answer:

y = 1/5x + 2 1/5

Step-by-step explanation:

first find the negative reciprocal slope of 5x + y = 30 because perpendicular lines have negative reciprocal slope:

=> y = -5x + 30, negative reciprocal of the slope -5 is 1/5

substitute the new slope 1/5 and the coordinate (9, 4) into the equation: y = mx + b to solve for b

=> 4 = 1/5(9) + b

=> 4 = 9/5 + b

=> b = 2 1/5

plug in the slope 1/5 and b = 2 1/5 into the equation: y = mx + b

=> y = 1/5x + 2 1/5

Which of these are integers?
-10
27
-1.33
-0.50
-65

Answers

Answer:

postive integer

negative integer

-10 and -65

Step-by-step explanation:

integers are whole numbers thats are not fractions or decimal. They can be negative as well but if you want a positive integer then the answer is 27

how do I do the work by myself??

Answers

Answer: By doing it with your notes or you could ask help from the teacher? You don't have a problem on here so good luck.

The dimensions of a rectangle are 2 x − 5 and 3 x + 3 . Which expression represents the area of the rectangle in simplest terms? A. 6 x 2 − 9 x − 15 B. 6 x 2 − 9 x + 15 C. 6 x 2 + 9 x − 15 D. 6 x 2 − 15 x − 9

Answers

Answer:

Step-by-step explanation:

The area of a rectangle is the product of its dimensions, that is

A = (2x - 5)(3x + 3) ← expand using FOIL

= 6x² + 6x - 15x - 15 ← collect like terms

= 6x² - 9x - 15 → A

What is the surface are of the cylinder with a height 7ft and radius 3ft?

Answers

Answer:

Total area, including top and bottom: 67.7 ft²

Step-by-step explanation:

The area of the sides (only) is A = (circumference of base)(height of cylinder), and in this case A = 2(3 ft)(3.14), or

approximately A = 18.8 ft²

If you also want the areas of the base and top of the cylinder, perform the indicated calculations:

A (top and bottom) = 2π(3 ft)² = 48.9 ft²

So that the total surface area is (48.9 + 18.8) ft², or 67.7 ft²

Please Helpppppppppppppppppppp

Answers

Answer:

See below

Step-by-step explanation:

[tex](f+g)(2)=f(2)+g(2)=7+3=10[/tex]

[tex](f-g)(4)=f(4)-g(4)=11-15=-4[/tex]

[tex](f \div g)(2)=7 \div 3 = \frac{7}{3}[/tex]

[tex](f \times g)(1)=f(1)\timesg(1)=5\times 0=0[/tex]

Josie is picking apples. She has 3 identical baskets that she is trying to fill. One basket is 3/5 full, another is 7/10 full, and the last is 2/3 full. What portion of the 3 baskets has Josie filled? Give you answer as a mixed number and as an improper fraction.

Answers

Answer:

1 29/30 full

Step-by-step explanation:

Basket 1 = 3/5 full

Basket 2 = 7/10 full

Basket 3 = 2/3 full

Total = 3/5 + 7/10 + 2/3

= (18+21+20) / 30

= 59/30

= 1 29/30 full

Therefore, the portion of the 3 baskets Josie has filled is 1 29/30

HELP ASAP!!! PLEASE IT'S DUE AT 4:00PM TODAY PLEASE!

Describe the difference between a Non-Linear Form and a Neither Linear, Nor Non-Linear Form.

Answers

Answer:

Linear means something related to a line. All the linear equations are used to construct a line. A non-linear equation is such which does not form a straight line. It looks like a curve in a graph and has a variable slope value.

Step-by-step explanation:

List 1 value that would make this inequality true.
9 - n ≥ 4

(How did you solve this)

Answers

9-1 > 4 = 8>4
This shows that 8 is greater than 4

8 is greater than 4 (9-1>4)

If one of the angles in a triangle is 55 degrees then what are possible measurements of the other two angles?

Answers

Answer:

100° and 25°

Step-by-step explanation:

Total measure of the angles in a triangle is 180°

180 - 55 = 125

split 125° into 2

lots of possible answers

the distance a plane travels between two cities is 260 miles. The same trip, in miles, traveled by car is approximately 10% greater due to the route traveled. If the car travel at an average rate of 55 miles per hour, approximately, how long will it take the car to travel between the same two cities?

Answers

Answer:

5.2 hours or 312 minutes

Step-by-step explanation:

The plane route has been given as 260 miles.

We're told that the car/road rouge is 10% longer, and that is 260 * 1.1, which is equal to 286 miles.

Now, the car travels at 55 miles per hour, and we're to calculate how long it will take to travel.

Speed = distance / time

Making time the subject of formula, we know that

Time = distance / speed

Time = 286 miles / 55 miles per hour

Time = 5.2 hours, converting to minute, we have 5.2 * 60 = 312 minutes.

A string of holiday lights at a store have three colors that flash at different
times. Red lights flash every fifth second. Blue lights flash every third
seconds. Green light flashes every four seconds. The store owner turns on
the lights. After how many seconds will all three lights flash at the same
time for the first time?

Answers

Answer:

30 times i think i don't know i am doing lcm and gcf

Step-by-step explanation:

I added question and example. answer it CORRECTLY and you will get brainliest!

Answers

Answer:

1008

Step-by-step explanation:

like the 2nd picture we split it in 3 rectangular prism

[tex]V_{1}[/tex]=6*7*8=336

[tex]V_{2}[/tex]=6*7*8=336

[tex]V_{3}[/tex]=6*7*8=336

V=336+336+336=1008

Solve for X

A) 5
B) 6
C) 7
D) 4

Answers

Answer:

A) 5

Step-by-step explanation:

ratio of big triangle to small is 9:5

45/9=5

5x/5=x

x=5

is the following number rational or irrational ? -0. overline 32

Answers

Answer:

yes

Step-by-step explanation:

because -0 is not rational number

How much more time did he spending watching T.V. and Talking on the phone than he did Going to School

Answers

Answer:

the answer is h 8ours

Answer:

who is he

Step-by-step explanation:

True or False: you can only multiply exponents when the bases are the same

Answers

Answer:

We are given that when two variables with same base are multiplied then the exponents will be add. We have to find that given statement is true or false. There are two variable with same base x therefore, the power will be added. Hence, the statement is true. Step-by-step explanation:

hope this helps god bless u and have a good day and give me brainliest if u want bye ;D

Answer:

True

Step-by-step explanation:

Josh is examining a set of data, and the standard deviation is 5.4. Josh finds a piece of data that was not included in the original set. He determines that the new data value is an outlier whose value is far below the other values in the set.

What will happen to the standard deviation of josh includes the new data value in the set?

Answers

Answer:

It will increase it.

Step-by-step explanation:

i go to primavera :)

5)
Which fraction is equivalent to 1/4
A 2/6 b 4/16 c 4/1 d 4/8

Answers

Answer is: 4/16 (please make me braniest!)

addison has 26 cups of cat food and 31 cups of dog food. Addison wants to use the same amount of cat food each day to feed her cats. she wants to use all the cat food she has before buying more. which statement is true?

Answers

Answer:

Who knows

Step-by-step explanation:

The question doesn't make sense so tell your teacher

The Marching band enters the gym and marches across the gym without turning. Which of these describes the transformation?
A. Dilation
B. Reflection
C. Rotation
D. Translation

Answers

Answer:

The answer is not c, it is b.

Step-by-step explanation:

They do not turn, so it is just a reflection. They are mirroring where they were before they moved.

Transformation involves changing the position of an object.

The transformation in this scenario is translation

From the question, we understand that:

The marching band marches across the gymAnd they did not turn

The above points simply mean that, they moved across the gym in a straight direction.

A movement on a straight line represents translation.

Hence, the correct transformation is (d) Translation

Answers

Answer: 24 bracelets.

Step-by-step explanation:

This question is about the division of numbers.

Since there are 3 yards of thread that is needed to be cut into pieces that are 1/8 of a yard long, this means that we've to divide 3 yards by 1/8. This will be:

= 3 ÷ 1/8

= 3 × 8

= 24

Therefore, they can make 24 bracelets from the yarn.

The population of a town is 4,000 people. Every year the population increases by 4%. What will the population of this town be after 7 years?
After 7 years the population of this town will be?

Answers

Answer:

The answer is 5,120

Step-by-step explanation:

How to find 4% of 4000:

4 times 4000=

16000 divided by 100

160

Then you add 160 to 4000 7 times and you get 5,120.

Answer:

p=c(1+r)^t the population in 7 years will be 5263.72711694

Step-by-step explanation:

p=c(1+r)^t

p=4,000(1+.04)^t

p=4,000(1.04)^t

p=4,000(1.04)^4

p=4679.43424

p= the population you are solving for

c= the initial amount of the population

(1+r)= the rate of change

t= the period of time

Find the area of the circle that contains the sector described below. Round to the nearest tenth, if necessary.

One sector has an area of 325 square millimeters and an arc measure of 72°.

__ mm2

Answers

If One sector has an area of 325 square millimeters and an arc measure of 72° then the area of circle is 1625 square mm.

What is Circle?

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

To find the area of circle we have to know the radius of the circle.

We know Area of sector=(θ/360º) × πr²

325=72/360×3.14r²

325=0.2×3.14r²

325=0.628r²

Divide both sides by 0.628

r²=517.51

Area of circle= πr²

=3.14×517.51

=1625 square mm.

Hence, if One sector has an area of 325 square millimeters and an arc measure of 72° then the area of circle is 1625 square mm.

To learn more on Circles click:

https://brainly.com/question/11833983

#SPJ1

Use the following data to answer the question
10, 9, 4, 7,5.5
The range for this data is
10
06
05
04

Answers

Answer:

Step-by-step explanation:

range is the highest data

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