A. The approximate height of the building is 100 m
B. We can use the arc length formula to obtain an approximation of BC since angle A is small.
A.
The approximate height of the building is 100 m
To find the approximate height of the building, we consider the diagram.
From the diagram, we have that using trigonometry,
tanA = BC/AB
Now
- A = 0.05 radians,
- BC = height of building and
- AB = 2 km = 2000 m
Finding the value of BC
So, making BC subject of the formua, we have
BC = ABtanA
Substituting the values of the variables into the equation, we have
BC = ABtanA
BC =2000tan0.05
BC = 2000 × 0.05
BC = 100 m
So, the approximate height of the building is 100 m
B.
We can use the arc length formula to obtain an approximation of BC since angle A is small.
Arc Length Formula
We know that the arc length formula L = rФ where
- r = radius and
- Ф = angle in radians
The approximate height
Now BC = ABtanA
We know that Ф ≅ tanФ when Ф is small.
The comparison
So, BC = AB × A which is the arc length formula with
So, we can use the arc length formula to obtain an approximation of BC since angle A is small.
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