Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

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

Aug 29, 2015

$| P Q | = 37.84881$ $|PQ| = 37.84881$ meters

Explanation:

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

$XXX | Q B | = 205 \cdot cot (36^{\circ})$ $color(white)("XXX")|QB| = 205*cot(36^@)$

$XXX | P B | = 205 \cdot cot (40^{\circ})$ $color(white)("XXX")|PB| = 205*cot(40^@)$

enter image source here

Using a calculator (for $cot (36^{\circ})$ $cot(36^@)$ and $cot (40^{\circ})$ $cot(40^@)$ )
$XXX | Q B | = 282.1583$ $color(white)("XXX")|QB| =282.1583$ meters

$XXX | P B | = 244.303095$ $color(white)("XXX")|PB|=244.303095$ meters

$\to XXX | Q P | = 37.84881$ $rarrcolor(white)("XXX")|QP|= 37.84881$ meters

Related questions

See all questions in The Law of Sines

Impact of this question

3663 views around the world

You can reuse this answer
Creative Commons License