Answer:
height of building 2 ≈ 104 m(nearest metre)
Step-by-step explanation:
The angle of elevation from the top of the shorter building to the top of the taller building is 25°.The angle of depression from the top of the shorter building to the base of the taller building is 30°. The height of building 2 (taller building) is the sum of the height of building 1 plus the height from the roof of building 1 where the angle of elevation was measured to the topmost layer of building 2.
The height of building 1 can be calculated using the tangential properties of the right angle triangle formed. The adjacent side is 100 m while the opposite side is the height of building 1.
tan 30° = opposite/adjacent
tan 30° = height of building 1/100
height of building 1 = 100 tan 30°
height of building 1 = 100 × 0.57735026919
height of building 1 = 57.735026919
height of building 1 = 57.74 m
The angle of elevation from the top of building 1 to the top of building 2 forms a right angle triangle .
using tangential ratio
tan 25° = opposite/adjacent
tan 25° = height from the top of building 1 to the topmost layer of building 2/100
height from the top of building 1 to the topmost layer of building 2 = 100 tan 25°
height from the top of building 1 to the topmost layer of building 2 = 100 × 0.46630765815
height from the top of building 1 to the topmost layer of building 2 = 46.6307658155
height from the top of building 1 to the topmost layer of building 2 = 46.63 m
Height of building 2 = 46.63 + 57.74 = 104.37 m
height of building 2 ≈ 104 m
