Question

A guy-wire is attached to a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the length of the guy wire (round to 2 decimal places)?. . A) 58.15 feet. . B) 143.40 feet. . C) 148.83 feet. . D) 350.62 feet

Answer 1

Answer: The correct option is 350.62 feets.

Step-by-step explanation:

Let the triangle Δ ABC

the length of wire = AC

Height of the pole  = AB

Length between the point of attachment of wire from base of the pole = BC = 137 feets

Angle of elevation to the pole = θ = 67 °

According to trigonometry :

cosθ = $\frac{base}{hypotenuse}$

cos 67 ° = $\frac{BC}{AC}$

$0.39=\frac{137}{AC}$

AC = 351.28 feets $\approx$ 351 feets.

From the given option the closest value to our answer is 350.62 feets.

Hence, the correct option is 350.62 feets.

Answer 2

Answer: For this diagram, the answer is D) 322.75 feet

Step-by-step explanation:

Since this is a right triangle and you know the angle and the adjacent side, use tan(x) = opp/adj

tan 67° = x/137

x = 322.75