An observer that is on the ground at point A watches a rocket ascend from the point B. The observer is 1200 feet from launch point B.
As the rocket rises, the distance d from the observer to the rocket increases. We want to express m ∠A in terms of d. To do so, we can use the trigonometric ratio for cosine.
cos θ = Adjacent/Hypotenuse
In our case, the length of the adjacent leg is 1200 and the hypotenuse is the distance between the observer and the rocket.
cos θ = Adjacent/Hypotenuse
⇓
cos A = 1200/d
We will find an expression for m∠A by applying the inverse cosine in each side of this equation.
cos A = 1200/d
⇓
m∠A = cos^(- 1) ( 1200/d )
b
We want to find the value of m∠A when the distance is 1500 feet. To do so, we will use the expression found in Part A.
m∠A = cos^(- 1) ( 1200/d )
We will substitute 1500 for d in this formula and then we will evaluate it to find the value of m∠A. Let's do it!
