Question

If the distance from the boat to the lighthouse is 120 meters and the angle of elevation is 40°, which of the following equations will find the height of the lighthouse? A right triangle is formed from the distance between a boat and the bottom of a lighthouse, the height of the lighthouse, and the distance from the boat to the top of the lighthouse; the angle of elevation from the boat to the top of the lighthouse is x degrees. Cos 40° = 120 over 7 cos 40° = y over 120 tan 40° = 120 over 7 tan 40° = y over 120.

Answer 1

You can use the fact that lighthouses are usually standing perpendicular to the ground that smaller distance on earth surface(planes or water bodies like sea or ocean or calm river) acts as if they a straight plane.

The length (y) of the lighthouse is given by:

Option D:  tan 40° = y over 120.

What is angle of elevation?

What you see something higher than your eye level height, you need to see up, you elevate your head to see that thing. The angle from the straight horizontal level of eye to the current elevated level is measured and named as angle of elevation.

Similarly, there is angle of depression when the observer looks down.

How to calculate the height of the considered lighthouse?

See the figure attached below to understand the symbols used in calculations.

Let the boat is on point C, and let the light house be AB.

Then we have:

Length of CA = 120 meters

∠ ACB = 40°

To find: length of AB

By using the trigonometric ratio tangent, we get:

$tan(\angle ACB) = \dfrac{AB}{AC}\\\\tan(40^\circ) = \dfrac{h}{120}$

Since here h is denoted by y, we have h = y, or

The equation to find the height of the lighthouse is

$tan(40^\circ) = \dfrac{y}{120}$

Thus,

The length (y) of the lighthouse is given by:

Option D:  tan 40° = y over 120.

Learn more about angle of elevation here:

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