Answer: B
Step-by-step explanation:
We are given an angle and a distance, and to solve for the height we need to make a triangle.
First, I'm going to assign sides to the triangle:
Side a: This is going to be the distance from the camera to the launch pad.
Side b: This is going to be the distance from the launch pad to the rocket (the rocket's height)
Side c: This is going to be the distance from the rocket to the camera (this is the hypotenuse of the triangle)
Now that we have sides, we can solve for the height. The height is the distance from the launch pad to the rocket, so it will be side b. We know that the camera is 5000 ft away from the launch pad, so we can say that side a is 5000 ft. It also tells us the camera is angled up at 27 degrees, so we can say angle B is 27 degrees.
We have a known side that length that is adjacent to a known angle inside of a right triangle, and we want to find the length of the opposite side. In this situation we can use the function tangent.
tan(theta) = opposite / adjacent
If we plug values into this equation we get:
tan(B) = b / a
tan(27 degrees) = b / 5000
b = tan(27 degrees) * 5000
b = 2547.627
b rounded to the nearest foot is 2548 ft, which is answer B
