a tower and a monumement stand on a level plane. The angles of depression of the top and bottom of monument as viewed from the top of the tower are 13 degree and 31 degree respectively. If the height of the tower is 145 ft.,find the height of the monument
Did you make a diagram?
You can find every possible angle in both triangles, one is right angled.
Start with the right-angled triangle and find its hypotenuse.
Then use the Sine Law in the next triangle.
45ft
To find the height of the monument, we can use trigonometry and create a right triangle.
Let's label the height of the monument as 'h'. We know that the height of the tower is 145 ft.
From the top of the tower, the angle of depression to the top of the monument is 13 degrees. This forms a right angle with the height of the tower. Therefore, we have a right triangle with the height of the tower as the vertical side and the line of sight to the top of the monument as the hypotenuse.
Using trigonometry, we can use the tangent function:
tangent(angle) = opposite/adjacent
In this case, the angle is 13 degrees and the adjacent side is the height of the tower. So we have:
tangent(13 degrees) = h/145 ft
Now we can solve for 'h'. Rearranging the equation, we get:
h = tangent(13 degrees) * 145 ft
Using a calculator, we find:
h ≈ 40.16 ft
Therefore, the height of the monument is approximately 40.16 feet.