An observer on top of the building 66m high, finds the angle of elevation to the top of a taller building to be 34 degrees. The angle of depression to the foot of the same building is 51 degrees. If the building are on the same ground level find the height of the taller building.
AAAaannndd the bot gets it wrong yet again!
Excuuuuuuse mmmeeee!! If the shorter building is 66m tall, how can the taller building be 49.4m?
(h-66)/tan34° = 66/tan51°
h = 102.05
Let's call the height of the taller building "x".
From the observer's point of view, we can draw a right triangle where the adjacent side is the distance between the observer and the taller building (let's call this distance "d"), the opposite side is the height of the observer (66m), and the hypotenuse is the distance between the observer and the top of the taller building.
Using trigonometry, we know that:
tan(34) = x/d (since the angle of elevation is formed by the opposite and adjacent sides)
tan(51) = x + 66/d (since the angle of depression is formed by the adjacent and opposite sides)
We can solve this system of equations for x and d:
x = d tan(34)
x + 66 = d tan(51)
Now we can substitute the first equation into the second equation:
d tan(34) + 66 = d tan(51)
Simplifying:
d = 66 / (tan(51) - tan(34)) ≈ 84.7m
Now we can use the first equation to find x:
x = d tan(34) ≈ 49.4m
Therefore, the height of the taller building is approximately 49.4m.