Sketch a diagram describing the given situation. Then recall the definition of the inverse tangent.
≈ 15^(∘)
Practice makes perfect
We are given that Tom delivers papers on a rural route and that he throws a paper from a height of 4 feet and it lands 15 feet from the car. Let's sketch a diagram describing this situation. Let x represent the angle of depression at which Tom threw the paper.
To evaluate the value of x, we can use one of the inverse trigonometric ratios. Let's start with recalling that the tangent of ∠ A is the ratio of the leg opposite ∠ A to the leg adjacent ∠ A. Using this definition, we can create an equation for tanx.
tan x=4/15
Next we will recall that if ∠ A is an acute angle and the tangent of A is a, then the inverse tangent of a is the measure of ∠ A.
Let's rewrite our equation and solve for x using a calculator.
tan x=4/15 ⇓
x=tan^(-1)4/15≈ 15^(∘)
The angle of depression is approximately 15^(∘).
