A person was standing on a road near a mall. He was 1215 m away from the mall and able to see the top of the mall from the road in such a way that the top of a tree, which is in between him and the mall, was exactly in line of sight with the top of the mall. The tree height is 20 m and it is 60 m away from him. How tall (in m) is the mall?
Answer & explanation
Correct answer: option 3
⇒ In triangle DEC
⇒ tan\(\theta \) = \(\frac{20}{60}\) = \(\frac{1}{3}\)
⇒ In triangle ABC
⇒ tan\(\theta \) = \(\frac{AB}{1215}\)
⇒ \(\frac{1}{3}\) = \(\frac{AB}{1215}\)
⇒ AB = \(\frac{1215}{3}\) = 405m.
Therefore, the height of mall is 405m.