a We are asked to find how many feet the plane must rise to pass over the tower, which we will call h, when the plane has an angle of elevation of 1^(∘) and the tower is 25 000 feet away. Let's take a look at the given diagram of this situation.
Notice that we can use one of the trigonometric ratios to evaluate the value of h. Let's recall that in a right triangle the sine of ∠ A is the ratio of the leg opposite ∠ A to the hypotenuse. Using this definition, we can create an equation for sin 1^(∘).
sin 1^(∘)=h/25 000
Let's solve the above equation.
The plane must rise approximately 436 feet to pass over the tower.
b In this part we are given that planes cannot come closer than 1000 feet vertically to any object, and we found that the plane must rise approximately 436 feet to pass over the tower. This means that we need to add these two values to the initial altitude, 20 000 feet.
20 000+ 1000+436=21 436
The plane must fly at an altitude of approximately 21 436 feet in order to pass over the tower.
