Originally Posted by

**Archie Meade** You could even more quickly find the angles in the scalene triangle PTQ

with 180-48-132 and 180-(132+32)=16.

You only have a side belonging to the scalene triangle, |PQ|=180m.

The point Q hasn't been labelled

You have all angles of the rightmost right-angled triangle QRT,

and the large external one PRT, and also the scalene one, PTQ.

To find the height, you need a side length of the rightmost right-angled triangle QRT,

or the larger right-angled triangle PRT, in order to use sin, cos or tan.

We don't have a side of either of these,

hence we must work with the scalene triangle.

this means using the sine or cosine rule, which solve non-right-angled triangles.

The sine rule is the easier one to use,

we use it when we have a side length and the angle opposite this side.

We have |PQ|=180m and angle PTQ=16 degrees.

$\displaystyle \frac{sinA}{a}=\frac{sinB}{b}$

$\displaystyle \frac{a}{sinA}=\frac{b}{sinB}$

where A and B are 2 angles in a non-right-angled triangle

(it works for right-angled triangles too of course! but we usually use

the standard definitions for sin, cos and tan with those)

and "a" is the side opposite A,

"b" is the length of the side opposite angle B.