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 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.
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:
[tex]tan(\angle ACB) = \dfrac{AB}{AC}\\\\tan(40^\circ) = \dfrac{h}{120}[/tex]
Since here h is denoted by y, we have h = y, or
The equation to find the height of the lighthouse is
[tex]tan(40^\circ) = \dfrac{y}{120}[/tex]
Thus,
The length (y) of the lighthouse is given by:
Option D: tan 40° = y over 120.
Learn more about angle of elevation here:
brainly.com/question/12483071
Answer:
tan 40° = y over 120
Step-by-step explanation:
I just took the test :)
