The angles of elevation of a pole from two points which are 75 m and 48 m away from its base are α and β respectively. If α and β are complementary, then the height of the tower is
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 60 m
| Understanding | Application |
| Tricks |
According to question
let one angle is α So angle β = 90 - α |
| Now |
tanα = AC/BC ⇒ tanα = AC/48 .......i) ⇒ 48tanα = AC ......ii) & tan(90 - α) = AC/CD ⇒ 75cotα = AC .........iii) |
| Hence |
⇒ 48tanα = 75cotα ⇒ tan2α = 75/48 ⇒ tan2α = 25/16 ⇒ tanα = 5/4 (put the value in eq i) So ⇒ 5/4 = AC/48 ⇒ 5/4 × 48 = AC ⇒ AC = 60 m |
