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

Answer:

The distance between Tyrone and the piano is 23.7 yards

Step-by-step 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

$\frac{TD}{sin(P)}=\frac{TP}{sin(D)}$

substitute the given values

$\frac{15}{sin(38\°)}=\frac{TP}{sin(77\°)}$

$TP=\frac{15}{sin(38\°)}(sin(77\°))\\\\TP=23.7\ yd$

therefore

The distance between Tyrone and the piano is 23.7 yards