Sketch a diagram describing the given situation. Then recall the definition of the inverse tangent.
≈14.8^(∘)
Practice makes perfect
We are asked to find the angle of depression at which a pilot should land if his altitude is 528 feet and his horizontal distance to land is 2000 feet. Let's sketch a diagram describing this situation. Let x represent the angle of depression.
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=528/2000
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.
tan x=528/2000 ⇓
x=tan^(-1)528/2000
Finally, we will solve the equation using a calculator.
