I have a diagram in which AB is a vertical cliff. BC is a vertical building 80m in height. P is a point on level ground 200m away from A. The angle of elevation of the bottom of the building from P is 44 degrees. What is the angle of elevation of the top of the building from P?
I will assume that the building with side BC is on top of the cliff and A is at the bottom of the cliff.
step1:
tan44= AB/200
AB = 200tan44
so AC = 80 + 200tan44
let angle CPA = Ø
tanØ = AC/200 = (80 + 200tan44)/200
tanØ = 1.365
Ø = 53.79°
Thanks for your reply. The answer is correct!
To find the angle of elevation of the top of the building from point P, we can use the fact that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case, the opposite side is the height of the building BC, which is 80m. The adjacent side is the distance from P to the bottom of the building, which is 200m.
The tangent of an angle can be calculated using the formula tan(angle) = opposite/adjacent.
So, in this case, tan(angle) = 80/200.
To find the angle, we need to take the inverse tangent of both sides of the equation.
angle = arctan(80/200).
Using a calculator, we can find the angle to be approximately 20.56 degrees.
Therefore, the angle of elevation of the top of the building from point P is approximately 20.56 degrees.