-
Two persons are on either side of a temple, 75 m high, observe the angle of elevation of the top of the temple to be 30° and 60° respectively. The distance between the persons is :
-
- 173.2 metre
- 100 metre
- 157.7 metre
- 273.2 metre
Correct Option: A
AD = Height of temple = 75 metre
B and C ⇒ Positions of men
∠ABD = 30°; ∠ACD = 60°
In ∆ABD,
| tan 30° = | BD |
| ⇒ | = | √3 | BD |
⇒ BD = 75 √3 metre
In ∆ACD,
| tan 60° = | DC |
| ⇒ √3 = | DC |
| ⇒ DC = | = 25√3 metre | √3 |
∴ BC = BD + DC
= 75 √3 + 25 √3
= 100 √3 metre
= (100 × 1.732) metre
= 173.2 metre
