Question

A remote camera at ground level is filming the lift-off

of an Atlas rocket at a point 800 meters from the launch
pad. Let 0 be the angle of elevation to the rocket and let
s be the height of the rocket. Find 0 when s = 1500 meters.

Answer 1

The angle θ of elevation to the rocket when it is at a height of 1500 meters and 800 meters away from the camera is approximately 61.93°, calculated using the tangent trigonometric function.

Step-by-step explanation:

To calculate the angle theta (θ), which is the angle of elevation from the ground to the rocket when the rocket's height (s) is 1500 meters, we need to use trigonometric ratios. In this scenario, we can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle.

Tan(θ) = opposite/adjacent

Here, the opposite side is the height of the rocket (s = 1500 meters) and the adjacent side is the distance from the camera to the launch pad (800 meters).

Thus, Tan(θ) = 1500/800 = 1.875.

To find the angle of elevation θ, we take the arctangent (inverse tangent) of the ratio.

θ = arctan(1.875)

Use a scientific calculator or a trigonometry table to find that θ ≈ 61.93°.

Answer 2

Step-by-step explanation:

Use SOH CAH TOA.

Using TOA or tangent = tan0 = opp/adj.

tan0 = 1500m/800m -> tan0 = 1.875

Use inverse tan or tan^-1.

0 = tan^-1(1.875)

0 = 61.93 degrees.