Question

Two construction workers, Tyrone and Diego, are standing 15 yards apart, looking up at a piano hanging between the two men from a crane. Tyrone is staring at the piano with an angle of elevation of 65°, and Diego is looking up with an angle of elevation of 77°. What is the distance between Tyrone and the piano? Round the answer to the nearest tenth.

Answer 1

D

Explanation:

Edge 2020

Answer 2

The distance between Tyrone and the piano is 23.7 yards

Explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle P

Remember that the sum of the internal angles of a triangle must be equal to 180 degrees

∠T+∠D+∠P=180°

substitute the given values

65°+77°+∠P=180°

142°+∠P=180°

∠P=180°-142°=38°

step 2

applying the law of sines

`(TD)/(sin(P))=(TP)/(sin(D))`

substitute the given values

`(15)/(sin(38\°))=(TP)/(sin(77\°))`

`TP=(15)/(sin(38\°))(sin(77\°))\\\\TP=23.7\ yd`

therefore

The distance between Tyrone and the piano is 23.7 yards