A man 2 meters high observes the angle of elevation to the top of a building to be 61 degrees and the angle of depression to the bottom of the building to be 18 degrees. How tall is the building?

By using the **tangent **of the angles of elevation and depression, we can create two triangles. With some algebra, we can calculate the height of the top and the bottom parts of the building separately, then add them to get the total height. ;

Answered by MonteBlue | 2024-06-18

I've included a picture to illustrate.
We can see from the picture that we need to find side X of the triangle to be able to find side Y of the building. t an 18 = X 2 ​ X = t an 18 2 ​ X = 6.16 m
Now just find side Y: t an 61 = 6.16 Y ​ 6.16 t an 61 = Y 11.11 m = Y
Don't forget to add 2 m to 11.11 m for the total height of the building.
13.11 m is the height of the building.

Answered by a386 | 2024-06-24

The height of the building is approximately 13.11 meters after calculating the distances using trigonometric functions based on the angles of elevation and depression.
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Answered by a386 | 2024-09-30