Question

right triangles test #1 review
26.) a radio tower is supported by a wire that makes a 45° angle with the ground. how high up the tower does the 106 foot wire extend, how many yards from the base of the tower is the wire attached to the ground? (round both to the nearest tenth of a yard)
how high up? (square) yds
how far away? (square) yds

Explanation:

Step1: Convert wire to yards

Since 1 yard = 3 feet, convert 106 feet to yards:
$\text{Wire length (yards)} = \frac{106}{3} \approx 35.333$ yds

Step2: Find height on tower

Use sine for opposite side (height):
$\sin(45^\circ) = \frac{\text{Height}}{\text{Wire length}}$
$\text{Height} = 35.333 \times \sin(45^\circ) \approx 35.333 \times 0.7071 \approx 25.0$ yds

Step3: Find distance from base

Use cosine for adjacent side (distance):
$\cos(45^\circ) = \frac{\text{Distance}}{\text{Wire length}}$
$\text{Distance} = 35.333 \times \cos(45^\circ) \approx 35.333 \times 0.7071 \approx 25.0$ yds

Answer:

How high up? 25.0 yds
How far away? 25.0 yds