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?

1 Answer
Alan P.
Aug 29, 2015

|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^@)

enter image source here

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

Related questions
See all questions in The Law of Sines
Impact of this question
3659 views around the world
You can reuse this answer
Creative Commons License