What is the angle of depression from the top of a 500-foot cable that runs from a tower to a point 350 feet away?

First of all this needs to be recognized as a right triangle problem. The angle of depression is the angle outside the triangle that is complementary to the vertex angle (the angle at the top). Geometrically, this angle is congruent to the base angle inside the triangle (NOT the right angle). So we need to find the measure of the base angle to find the measure of the angle of depression since they are the same. A 500 foot cable describes the length of the cable, which serves as our hypotenuse. The 350 is the base length of the triangle. What we have then is a reference angle (x), the hypotenuse (500) and the side adjacent to the angle (350). The ratio that relates the angle to the hypotenuse and the adjacent side is the cosine. Setting up to find our angle gives us this equation:

[tex]cos\theta=\frac{350}{500}[/tex]

You find missing angles on your calculator by hitting the 2nd button and then the trig identity you want. We want cosine, so hit 2nd then cos and you'll get cos^-1( on your screen. After the parenthesis, enter your 500/350 and hit enter. This will give you your angle measure of 45.6. Oh yeah!!! And make sure your calculator is in degree mode for this one!

vintechnology vintechnology · Answer 2 · 2021-12-23T11:53:09+01:00

The angle of depression from the top of a 500-foot cable that runs from a tower to a point 350 feet away is 45.6 degrees

The situation forms a right angle triangle.

The length of the cable is the hypotenuse of the triangle formed.

The distance from the tower is the adjacent side of the right angle triangle.

Therefore, using trigonometric ratio,

let

∅ = angle of depression

cos ∅ = adjacent / hypotenuse

cos ∅ = 350 / 500

∅ = cos⁻¹ 0.7

∅ = 45.5729959992

∅ = 45.6°

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