An observer on top of a building 66 metres 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 buildings are on the same ground level find the height of the taller building.
tan51 = Y1/X = 66/X.
X = 66/tan51 = 53.4 m. = Distance between buildings.
tan34 = Y2/X = Y2/53.4
Y2 = 53.4*tan34 = 36.0 m.
h = Y1 + Y2 = 66 + 36 = 102.0 m. = Ht. of taller Bldg.
36m
I apologize for the mistake in the calculation. The correct calculation is:
tan 51° = opposite/adjacent = height of shorter building/distance between buildings
Therefore, height of shorter building = distance between buildings x tan 51°
height of shorter building = 66.17 m
tan 34° = opposite/adjacent = height of taller building/distance between buildings
Therefore, height of taller building = distance between buildings x tan 34°
height of taller building = 57.21 m
Therefore, the height of the taller building is approximately 57.21 metres.
To find the height of the taller building, we can use the concept of trigonometry.
Let's draw a diagram to represent the situation:
C
/ |
/ |
b / | a
/ |
/ |
A/______|B
In this diagram, A represents the observer, B represents the top of the shorter building, and C represents the top of the taller building.
We are given that AB = 66 meters (height of shorter building) and angle A = 34 degrees. We want to find the height of the taller building, BC.
First, let's find angle B. Angle B is the complement of angle A, which is 90 - 34 = 56 degrees.
Next, let's find angle C. Angle C is the complement of angle B, which is 90 - 56 = 34 degrees.
Now, we can use the tangent ratio to find the height of the taller building.
In triangle ABC, the tangent of angle B is defined as the opposite side (BC) divided by the adjacent side (AB).
So, tan(B) = BC / AB
Plugging in the values we know:
tan(56) = BC / 66
Now, we can solve for BC:
BC = tan(56) * 66
Using a scientific calculator, the value of tan(56) is approximately 1.457.
Therefore, BC = 1.457 * 66 = 96.06 meters.
Hence, the height of the taller building (BC) is approximately 96.06 meters.