Question

A surveyor is interested in determining the height of a tree. The angle of elevation of the top of the tree is 42°. The distance of the tree from the surveyor is 15cm. How tall is the tree?

Answer 1

To find the height of the tree, we can use trigonometry.

Let the height of the tree be \( h \). Then, we can set up the following equation using the tangent function:

\[ \tan(42^\circ) = \frac{h}{15} \]

Solving for \( h \), we get:

\[ h = 15 \times \tan(42^\circ) \]
\[ h = 15 \times 0.9004 \]
\[ h \approx 13.506 \ cm \]

Therefore, the height of the tree is approximately 13.506 cm.