Question

Naledi stands 42m from the base of the building. Her distance from the top of the building is 63m. What is the angel of elevation to the building

Answer 1

To find the angle of elevation to the top of the building from Naledi's position, we can use the tangent function from trigonometry. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the building) to the adjacent side (distance from the base of the building).

Let:
- \( h \) = height of the building
- \( d \) = distance from the base of the building = 42 m
- \( d_t \) = distance to the top of the building = 63 m
- \( \theta \) = angle of elevation

Using the Pythagorean theorem, we can express the relationship between these values:

\[
d_t^2 = h^2 + d^2
\]

Substituting the known values:

\[
63^2 = h^2 + 42^2
\]

Calculating the squares:

\[
3969 = h^2 + 1764
\]

Now, we can isolate \( h^2 \):

\[
h^2 = 3969 - 1764 = 2205
\]

Next, take the square root to find \( h \):

\[
h = \sqrt{2205} \approx 47.0 \text{ m (rounded to one decimal place)}
\]

Now, we can find the angle of elevation \( \theta \) using the tangent function:

\[
\tan(\theta) = \frac{h}{d} = \frac{47}{42}
\]

Calculating \( \tan(\theta) \):

\[
\tan(\theta) \approx 1.119
\]

Now, to find \( \theta \), we take the arctangent:

\[
\theta = \tan^{-1}(1.119) \approx 48.37^\circ
\]

Thus, the angle of elevation to the top of the building is approximately \( 48.37^\circ \).