The angle of depression of a point on the ground, situated at a distance of 10 metres from the base of a tree, from the top of the tree is 45°. The height of the tree will be:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 10 metres
The angle of depression from the top A of the tree to the point C equals the angle of elevation of A from C (alternate angles, since the horizontal through A is parallel to the ground). In right triangle ABC, \(\tan C=\frac{\text{AB}}{\text{BC}}\).
\(\displaystyle\tan45^\circ=\frac{\text{AB}}{10}\)
\(\tan45^\circ=1\), so AB \(=10\) m
Tip: At an angle of 45° the height and the distance are always equal, since \(\tan45^\circ=1\).