Exercise 1 Page 867

We are told that after traveling 800 yards horizontally, a plane has climbed 285 yards vertically. Knowing that it climbs at a constant rate, we want to find its angle of elevation during the takeoff and initial climb. Let's start by sketching a model of the problem. We will call the missing angle measure θ.

Since the plane has traveled horizontally and then vertically, we know that the triangle that we drew is a right triangle. We want to find the measure of one of its acute angles. Note that we are given the opposite and the adjacent sides to the unknown angle. Therefore, to find its measure we can use the tangent ratio. tan θ = Length of leg opposite toθ/Length of leg adjacent toθ In our triangle, the lengths of the opposite and adjacent legs to θ are 285 and 800.

tan θ = Opposite/Adjacent

SubstituteII

opposite= 285, adjacent= 800

tan θ = 285/800

ReduceFrac

a/b=.a /5./.b /5.

tan θ = 57/160

The tangent of the angle is 57160. Now, to isolate θ we will use the inverse function of tan. tan θ=57/160 ⇔ θ=tan ^(- 1)57/160 Let's use a calculator to find the value of tan ^(- 1) 57160. First, we will set our calculator into degree mode. To do so, push MODE, select Degree instead of Radian in the third row, and push ENTER. Next, we push 2ND followed by TAN, introduce the value 57160, and press ENTER.

The angle of elevation of the plane is about 19.6^(∘), which corresponds to option C.