SOLUTION: Two boats, 70 meters apart and on the opposite sides of a light house, are in a straight line with the light house. The angles of elevation of the top of the light house from the t

Algebra ->  Trigonometry-basics -> SOLUTION: Two boats, 70 meters apart and on the opposite sides of a light house, are in a straight line with the light house. The angles of elevation of the top of the light house from the t      Log On


   

Question 1114649: Two boats, 70 meters apart and on the opposite sides of a light house, are in a straight line with the light house. The angles of elevation of the top of the light house from the two boats are 71.6° and45°. Find the height of the light house. ( Take tan 71.6°= 3)
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Two right triangles with same height, y.
The farther boat, x meters from the bottom.
The nearer boat, 70-x meters from the bottom.

system%28y%2Fx=tan%2871.6%29%2Cy%2F%2870-x%29=tan%2845%29%29

One tangent value is given and the other is of a commonly known angle.

system%28y%2Fx=3%2Cy%2F%2870-x%29=sqrt%282%29%2F2%29
Solve for x from one equation and substitute into the other equation. Solve for the value of y.