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In Mathematics / High School | 2014-10-27

Use the Pythagorean theorem and/or trigonometry to solve the following word problem.

Layne spots a sailboat from her 5th-floor balcony, about 25 m above the beach, at an angle of depression of 3 degrees. To the nearest meter, how far out is the boat?

Asked by Foxhunter80

Answer (2)

I'm going to use just trig for this one.
so basically, you're going to find the adjacent side of a triangle by using the other side, so you would use tangent.
T an 30 = X 25 ​
then just rearrange and solve for X
X = T an 30 25 ​
And the answer is 43.3 i think.
If i'm wrong please correct me

Answered by Mexequin | 2024-06-10

Using the Pythagorean theorem and trigonometry, we find that the boat is approximately 477 meters away from the base of Layne's building. The height from her balcony was used in conjunction with the angle of depression of 3 degrees to calculate this distance. The calculation involves using the tangent function based on the right triangle formed by the observation setup.
;

Answered by Mexequin | 2024-12-26

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