Lauren was at the pier at the beach approach trying to find her sister. She saw her at the water's edge at an angle of depression of 12 degrees .

Question

If the pier is 5 yards above the sand, how far down the beach is Lauren's sister?Round your answer to the nearest yard.

help please,also do it step by step please

Answer 1

If the angle of depression from the pier to the beach is 12 degrees, then the angle of elevation from the beach to the pier is also 12 degrees.

The height of the pier, distance along the beach and distance from the beach to the top of the pier form a right triangle, so we will be able to use trigonometric functions of a right triangle to solve this problem.

The side opposite the angle of elevation is the height of the pier 5 yds. The adjacent side to the angle of elevation is the distance down the beach from the pier we are trying to find.

Tangent (12) = opposite/adjacent = 5/adjacent

so adjacent = 5/tangent(12) = 23.5 yards, which is how far Lauren's sister is diown the beach.

Answer 2

Hi Lauren,

You can draw the right triangle to solve this problem.

The height 5 yards will be your opposite side, and you have to find the length of adjacent side to find how far Lauren's sister is. If you see the triangle you will notice that the from the point where Lauren's sister is it will be the angle of elevation, which is the equal to the angle of depression from the pier, the reason for that is: you have two parallel lines cut by the transversal (here hypotenuse of right triangle), then the alternate interior angles are congruent.

Use tan (12) = opposite / adjacent to solve

Hope this helps.