<h2>A 30-meter high building sits on top of a 151.52 meter high hill.</h2>
Explanation:
According to the given data, we can draw a figure (Please refer the attachment below)
Building's height = 30 meter
Angle of elevation from a spot to the top of the building = 55 degrees
Angle of elevation from the spot to the top of the building = 50 degrees
To find the height of the hill, we need to use the formula,
![tan \,\theta = \frac{opposite \,side}{adjacent \,side}](https://tex.z-dn.net/?f=tan%20%5C%2C%5Ctheta%20%3D%20%5Cfrac%7Bopposite%20%5C%2Cside%7D%7Badjacent%20%5C%2Cside%7D)
then, ![tan \,50 = \frac{h}{x}](https://tex.z-dn.net/?f=tan%20%5C%2C50%20%3D%20%5Cfrac%7Bh%7D%7Bx%7D)
![\Rightarrow x = \frac{h}{tan 50}](https://tex.z-dn.net/?f=%5CRightarrow%20x%20%3D%20%5Cfrac%7Bh%7D%7Btan%2050%7D)
.... (1)
Similarly, ![tan \,55 = \frac{30+h}{x}](https://tex.z-dn.net/?f=tan%20%5C%2C55%20%3D%20%5Cfrac%7B30%2Bh%7D%7Bx%7D)
![\Rightarrow x = \frac{30+h}{tan 55}](https://tex.z-dn.net/?f=%5CRightarrow%20x%20%3D%20%5Cfrac%7B30%2Bh%7D%7Btan%2055%7D)
.... (2)
(1) = (2) becomes
![\frac{h}{1.192} = \frac{30+h}{1.428}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bh%7D%7B1.192%7D%20%3D%20%5Cfrac%7B30%2Bh%7D%7B1.428%7D%20)
[tex]\Rightarrow [tex] 1.428h = (30 + h)1.192
1.428h = 35.76 + 1.192h
1.428h - 1.192h = 35.76
0.236h = 35.76
h = 151.52 meter
Therefore, the hill highs 151.52 meter.