Question

A 500-foot cable is attached to the top of a tower and is stretched tight to a point that is 350 feet away from the base of the tower. What is the angle of depression formed by the cable? A. 34. 9° B. 35. 3° C. 44. 4° D. 45. 6°

Answer 1

The angle of depression the cable forms is the arctan of the ratio of the

horizontal distance to the height of the tower which is approximately 35°.

Response:

B. 35°

Which method can be used to find the angle of depression?

Given:

Height of the tower = 500-feet

Horizontal distance from the (other)  point of attachment of the cable to

the base of the tower = 350-feet.

Required:

The angle of depression formed by the cable.

Solution:

The angle of depression is the angle, θ, the cable forms with the tower

from the top of the tower.

By trigonometric ratios, therefore;

$tan(\theta) = \mathbf{\dfrac{Horizontal \ distance \ of \ cable \ from \ tower}{Height\ of \ tower}}$

Which gives;

$tan(\theta) = \dfrac{350}{500} = \dfrac{7}{10}$

• $Angle \ of \ depression, \ \theta = \mathbf{ arctan \left(\dfrac{7}{10} \right) }\approx35^{\circ}$

The best correct option is; B. 35°

Learn more about trigonometric ratios here:

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