Question

Find the exact values for the lengths of the labeled segments a, b and p drawn in green, red, and blue, respectively. Note that r = 5 is the radius of the circle, and s = 4 is the arc length from the point (5,0) around the circle to the indicated point.

Answer 1

somehow I can't see the red, green and blue labels

Answer 2

\(\bf \textit{Arc's Length}=s=\cfrac{radius\cdot angle\cdot \pi}{180}\\ \quad \\
4=\cfrac{5\cdot \theta\cdot \pi}{180}\implies \cfrac{4\cdot 180}{5\cdot \pi}=\theta\)

once the angle is found, you can use \(\bf cos(\theta)=\cfrac{a}{5}\implies 5cos(\theta)=a\qquad sin(\theta)=\cfrac{b}{5}\implies 5sin(\theta)=b\)

Answer 3

but tan(90) is undefined