precalculus question using trigonometry

Question

A rocket is fired from the ground at an angle of 0.88 radians. Suppose the rocket has traveled 400 yards since it was launched. Draw a diagram and label the values that you know. how do you find how far the rocket went horizontally and vertically?

Answer 1

Draw and label a diagram. The distance the rocket travels will form the hypotenuse. From there, you should see that the vertical height forms the opposite side of the triangle and the horizontal distance forms the adjacent side of the triangle with the angle of interest formed between the ground and the rocket distance. Then, it's just a matter of using the correct trig functions and solving for the unknown sides.

Here's how to find the vertical height:

Sine is the right choice because it involves the hyp, which you know, and the opp is the vertical height that you want to find

sin(angle) = opp / hyp

I'll represent the vertical height with y since that is traditional for vertical (x for horizontal)

sin(0.88) = y / 400

Isolating y you get: y = 400*sin(0.88) --- I multiplied both sides of = by 400 to isolate y

Evaluating the sine function with your calc in rad mode and multiplying you get y = 6.14 yards

For the horizontal distance, choose the trig function that uses the information you have and solve for what you don't similarly to the vertical (different trig function, though, if it isn't obvious)