The angle of elevation of the top of a building is 25 from a point 70m away on a level ground. Calculate the height of the building
To solve this problem, we can use the concept of the tangent function.
Let's call the height of the building "h".
From the problem, the angle of elevation is 25 degrees and the distance from the point to the base of the building is 70m.
Using the tangent function:
tan(angle) = opposite/adjacent
In this case, the opposite side is the height of the building (h), and the adjacent side is the distance from the point to the base of the building (70m).
So we can write the equation:
tan(25) = h/70
Now, multiply both sides of the equation by 70 to isolate the height:
70 * tan(25) = h
Using a calculator, we find that tan(25) is approximately 0.4663.
So the equation becomes:
70 * 0.4663 = h
Simplifying the equation, we get:
h = 32.64
Therefore, the height of the building is approximately 32.64 meters.