Sketch a diagram describing the given situation. Then recall the definition of the inverse tangent.
≈ 16.6^(∘)
Practice makes perfect
We are asked to find the angle of depression x from the center of the Akashi Kaikyo Bridge to the platform, and we know that the height from the top of the platform is 297 meters and that the length from the platform to the center of the bridge is 995 meters. Let's sketch a diagram describing this situation.
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=297/995
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=297/995 ⇓
x=tan^(-1)297/995
Finally, we will solve the equation using a calculator.
