Two cables, with lengths of 40 feet and 35 feet, are tied from the top of a pole to stakes in
the ground. If the stakes are 30 feet apart, find the height of the pole.

Answer:

The height of the pole is 33.89 feet.

Step-by-step explanation:

Since the length of the cables are 35 feet and 40 feet respectively, the 40 feet cable being farthest from the pole. We know that they are 30 feet apart. This forms a scalene triangle in which the angle between the 40 feet cable and the distance apart of the cables ( or ground) is the angle of elevation of the pole from the 40 feet cable.

So, we use the cosine rule to find this angle of elevation. So,

b² = a² + c² - 2accosB where a = 40 feet , b = 35 feet, c = 30 feet and B = angle of elevation of top of pole from 40 feet cable.

cosB = (a² + c² - b²)/2ac

cosB = (40² + 30² - 35²)/(2 × 40 × 30)

cosB = (1600 + 900 - 1225)/2400

cosB = 1275/2400

cosB = 0.53125

B = cos⁻¹(0.53125)

B = 57.9°

Since we now have the angle of elevation of the top of the pole from the 40 feet cable, we now find the height h of the pole from

sinB = h/40 since the 40 feet cable, the ground and the pole form a right-angled triangle.

h = 40sinB

h = 40sin57.9°

h = 40 × 0.8472

h = 33.89 feet

So, the height of the pole is 33.89 feet.

Which of the following values would complete the ordered pair if the point is on the graph of ƒ(x) = -2x + 3?



(-1, ___)

a. 1
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Adjust point D so the measure of angle BAD is equal to the measure of angle CAD. Which statements are true? Check all that apply.

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AD bisects BC.
AD forms right angles with BC.
AD is perpendicular to BC.
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2.

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4.

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Solve: -3 - (-5) + (-2)

​

Exercice 3
Une société propose sur le marché trois formats de cônes glacés : le grand, d'un volume de
720 mL, le moyen et le petit.
a) Le cône moyen est une réduction du grand dans le rapport 75 %. Calculer son volume.
b) Le petit cône est une réduction du grand cône dans le rapport 50 %.
Marie affirme : « Le volume du petit cône est deux fois plus petit que celui du moyen >>
Qu'en pensez-vous ?
Exercice 4
Le volume d'une boule lyonnaise est environ 378 cm! Son diamètre est le triple de celui du
<< but >>
Calculer une valeur approchée du volume du but.
Windows is not genuine
Click this message to learn how to get genuine
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10:38 PM
10/28/2020
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The first term in an arithmetic sequence is 5. The third term in the sequence is -1. The tenth term in the sequence is -22.
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A.
f(n) = -n

B.
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C.
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D.
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Lo

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