91Ó°ÊÓ

The height of a radio tower is $500$feet, and the ground on one side of the tower slopes upward at an angle of $10°$.

Let the top of the tower be A, base of the tower be B and the right point to be connected to the top of the tower be C.

Now, $b^2=a^2+c^2-2ac\cos B$

$={100}^2+{500}^2-2×100×500\cos 80°$

$=10000+250000-100000\cos 80°$

$b≈492.58$

So, a guy wire should be $492.58$feet long to connect the top of the tower and be secured at a point on the sloped side $100$feet from the base of the tower.

The height of a radio tower is $500$feet, and the ground on one side of the tower slopes upward at an angle of $10°$.

Let the middle of the tower be A, base of the tower be B and the left point to be connected to the top of the tower be C.

Now, $b^2=a^2+c^2-2ac\cos B$

role="math" localid="1647028188731" $={100}^2+{250}^2-2×100×250\cos 90°$

role="math" localid="1647028223053" $=10000+62500-50000\cos 90°$

$b≈269.26$

So, the second guy wire should be $269.26$feet long to connect the middle of the tower and be secured at a point $100$feet from the base on the flat side.