A person whose eye level is 1.5 meters above ground level looks at the top of a tree at an angle of 24° above the horizontal. If the tree is 20 meters away, how tall is the tree?

A person whose eye level is 1.5 meters above ground level looks at the top of a tree at an angle of 24° above the horizontal. If the tree is 20 meters away, how tall is the tree?

Answer:
Height of tree (to nearest half meter): 10.5 meters

Explanation:
Assuming the situation is as indicated in the image below:

The height of the tree is t+ 1.5m

\(\frac{t}{20 \mathrm{~m}}=\tan \left(24^{\circ}\right)\)

Therefore

\(\text { Height of tree }=20 \cdot \tan \left(24^{\circ}\right) \mathrm{m}+1.5 \mathrm{~m}\)

(with the aid of a calculator)
\(\begin{aligned}
&\approx 8.905+1.5 \mathrm{~m} \\
&\approx 10.4 \mathrm{~m}
\end{aligned}\)