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
[tex]\frac{TD}{sin(P)}=\frac{TP}{sin(D)}[/tex]
substitute the given values
[tex]\frac{15}{sin(38\°)}=\frac{TP}{sin(77\°)}[/tex]
[tex]TP=\frac{15}{sin(38\°)}(sin(77\°))\\\\TP=23.7\ yd[/tex]
therefore
The distance between Tyrone and the piano is 23.7 yards
