Let angle POQ be designated theta Angles PQR OSU and VRQ are

Let angle POQ be designated theta. Angles PQR, OSU, and VRQ are right angles. If theta = 20 degree, find the length of OU accurate to four decimal places.

Solution

angle POQ = 20 degrees

since angle SOR = 90 degrees

therefore, angle SOU = 90-20 = 70 degrees

length of OS = 1 , since coordinates of S are (0,1)

applying tan rule on triangle OSU ( right angle triangle )

tan 70 = SU / SO

2.7474 = SU / 1

SU = 2.7474

applying pythagorean theorem

OU^2 = SO^2 + SU^2

OU^2 = 1^2 + 2.7474^2 = 8.5482

OU = sqrt 8.5482 = 2.9237