If a wooden block is placed against a 15 meter tree such that it just reaches the top of the tree, with the angle of elevation of the tree is 30°, then find the length of the wooden block?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 30 meter
The tree, the ground and the block form a right triangle: the tree (15 m) is the side opposite the 30° angle and the block is the hypotenuse, so \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\) links them.
With \(L\) the length of the block: \(\displaystyle\sin30^\circ=\frac{15}{L}\)
\(\sin30^\circ\) is one half, so \(\displaystyle\frac{1}{2}=\frac{15}{L}\)
So the block is \(L=30\) m long, twice the height of the tree