SAT High School

In ΔUVW, u = 1.7 inches, v = 6.5 inches and ∠W=90°. Find the length of w, to the nearest 10th of an inch.

Answers

Answer 1

Answer: To find the length of side W (w) in the given triangle, we can use the Pythagorean theorem since we know that ∠W is a right angle.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

So, we have:

w^2 = u^2 + v^2

Substituting the given values:

w^2 = (1.7 inches)^2 + (6.5 inches)^2

w^2 = 2.89 + 42.25

w^2 = 45.14

Taking the square root of both sides to isolate w:

w = √45.14

Calculating this square root, we find:

w ≈ 6.71 inches

Therefore, the length of side W (w) in the triangle ΔUVW is approximately 6.71 inches, rounded to the nearest tenth of an inch.

Related Questions

In ΔPQR, r = 38 cm, m∠P=49° and m∠Q=127°. Find the length of p, to the nearest centimeter.

Answers

The length of side PQ is approximately 29 cm, rounded to the nearest centimeter.

How to calculate the value

In triangle PQR, we are given:

r = 38 cm (the length of side QR)

m∠P = 49° (angle P)

m∠Q = 127° (angle Q)

Let's find the length of side PQ:

sin(49°) / PQ = sin(127°) / 38 cm

Using the given information, we can substitute the values:

sin(49°) / PQ = sin(127°) / 38

To find PQ, we can cross-multiply and solve for it:

PQ = (sin(49°) * 38) / sin(127°)

Calculating this value:

PQ ≈ (0.7557 * 38) / 0.9996

PQ ≈ 28.6796 / 0.9996

PQ ≈ 28.693 cm

= 29 cm

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In ΔOPQ, o = 30 cm, p = 89 cm and q=95 cm. Find the measure of ∠P

Answers

Based on the information, the measure of ∠P is approximately 76.4 degrees.

How to solve the triangle

Applying the Law of Cosines to ∠P, we have:

p² = o² + q² - 2oq * cos(∠P)

Substituting the given values:

89² = 30² + 95² - 2 * 30 * 95 * cos(∠P)

7921 = 900 + 9025 - 5700 * cos(∠P)

Now, let's simplify the equation:

7921 = 9025 - 4800 * cos(∠P)

Rearranging the terms:

4800 * cos(∠P) = 9025 - 7921

4800 * cos(∠P) = 1104

cos(∠P) = 1104 / 4800

cos(∠P) = 0.23

Now, we need to find the inverse cosine (arccos) of 0.23 to determine the measure of ∠P.

∠P = arccos(0.23)

∠P ≈ 76.4 degrees

Therefore, the measure of ∠P is approximately 76.4 degrees.

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