Question

Given: LN ⊥ KM

LN = 16 ft

m∠K = 25°,m∠M = 55°

Find: Radius R

Answer 1

Full decimal:

~ 23.10879

Answer 2

23.1 ft

Explanation:

Consider right triangle LMN. In this triangle,

`m\angle M=55^(\circ)\\ \\LN=16\ ft`

By sine definition,

`\sin \angle M=\frac{\text{Opposite leg}}{\text{Hypotenuse}}=(LN)/(LM)=(16)/(LM)\\ \\LM=(16)/(\sin 55^(\circ))`

In triangle KLM, by sine theorem,

`(LM)/(\sin \angle K)=2R,`

where R is the radius of circumscribed circle.

Therefore,

`R=(1)/(2)\cdot ((16)/(\sin 55^(\circ)))/(\sin 25^(\circ))=(8)/(\sin 55^(\circ)\cdot \sin 25^(\circ))\approx 23.1\ ft`