Question

I’m confused on this one

Answer 1

AS would equal 4 units.

We must first mention that angle bisectors halve the angle that they bisect, so angle PAR = angle PAS. This means we can use the given information to find angle PAR, and then put that into triangle PAS and use trigonometry.

To find angle PAR, we must label the sides of triangle RPA to make AP, 5, the hypotenuse, and RP, 3, the opposite side. This means we need to use sine, and the trigonometric ratio sin(X) = (opposite/hypotenuse):

sin(X) = 3/5
${sin}^{ - 1}( \frac{3}{5}) \: = \: 36.87$

Then we look at triangle PSA and label AP, 5, the hypotenuse, and AS the adjacent. This means we need to use cosine, and the trigonometric ratio cos(X) = (adjacent/hypotenuse):

cos(36.87) = AS/5
× 5
cos(36.87) × 5 = AS
AS = 3.999995 = 4.00 to the nearest hundredth.

I hope this helps! Let me know if you have any questions :)