Answer:
distance of the rocket from the pine high school ≈ 344 miles
Step-by-step explanation:
The illustration forms a triangle with 2 right angle triangle in it. The western high school angle of elevation is 41° and the pine high school angle of elevation is 23°. The distance between the 2 school is 512 miles .The distance of the rocket from the pine school is the adjacent side of one of the right angle triangle .
The full triangle has angle of 23°, 41° and the last angle will be 180 - 23 - 41 = 116°. The hypotenuse side of the right angle triangle representing the pine high school triangle can be solved using sine formula.
p/sin 41° = 512/sin 116°
p/0.65605902899 = 512/0.89879404629
cross multiply
0.89879404629
p = 335.902222843
divide both sides by 0.89879404629
p = 335.902222843
/0.89879404629
p = 373.725464949
p ≈ 373.70 miles
using cosine ratio the adjacent side of the triangle can be found.
cos 23° = adjacent/hypotenuse
cos 23° = adj/373.70
cross multiply
adjacent = 0.92050485345 × 373.70
adjacent = 343.992663735
distance of the rocket from the pine high school = 343.992663735
distance of the rocket from the pine high school ≈ 344 miles
