Question

A smokestack, AB, is 205.0m high. From two points, P and Q, on the same side of its base B, the angles of elevation of A are 40 degrees and 36 degrees respectively. How do you find the distance between P and Q?

Answer 1

`|PQ| = 37.84881` meters

Explanation:

From the diagram below we can see that
`color(white)("XXX")|QP| = |QB| - |PB|`

`color(white)("XXX")|QB| = 205*cot(36^@)`

`color(white)("XXX")|PB| = 205*cot(40^@)`

Using a calculator (for `cot(36^@)` and `cot(40^@)`)
`color(white)("XXX")|QB| =282.1583` meters

`color(white)("XXX")|PB|=244.303095` meters

`rarrcolor(white)("XXX")|QP|= 37.84881` meters