Question

The top of a hill when observed from the top and bottom of a building of height h is at angles of elevation p and q respectively. What is the height of the hill?

पर्याय

• `("h"cot "q")/(cot "q" - cot "p")`

• `("h"cot "p")/(cot "p" - cot "q")`

• `(2"h"tan "p")/(tan "p" - tan "q")`

• `(2"h"tan "q")/(tan "q" - tan "p")`

Answer 1

`bb((hcot p)/(cot p - cot q))`

Explanation:

Let the height of hill = H

and horizontal distance between building and hill = d

tan q = `"H"/"d"`

`\implies` d = `"H"/tan"q"` = H cot q

tan p = `(("H" - "h"))/"d"`

`\implies` d = (H – h) cot p

`\implies` H cot q = (H – h) cot p

H = `(h cot "p")/(cot"p" - cot "q")`