Question

The height of a radio tower is 650 ​feet, and the ground on one side of the tower slopes upward at an angle of 10°.

Answer 1

Answer with Step-by-step explanation:

We are given that

Height of radio tower =650 ft

From figure

AB=650 ft

BC=180 ft

We have to find the AC.

Using cosine law:

$c=\sqrt{a^2+b^2-2ab cos\alpha}$

$AC=\sqrt{(650)^2+(180)^2-2\times 650\times 180\times cos 80^{\circ}}$

$c=643.64 ft$

Hence, a guy required 643.64 ft wire when it is to connect to the tower and be secured at  a point on the sloped side 180 ft from the base of the tower.

b.In a right triangle ABC, AB=$\frac{650}{2}=325 ft$

Pythagorous theorem :$(Hypotensuse)^2=(perpendicular\;side)^2+(base)^2$

Substitute the values

$(AC)^2=(AB)^2+(BC)^2$

$(AC)=\sqrt{(325)^2+(180)^2}$

$AC=371.52 ft$

Hence, the length of wire should be 371.52 ft when a second guy connect  the middle of the tower and be secured at a point 180 ft from the base on the flat side by wire.