In ΔNOP, the measure of ∠P=90°, the measure of ∠N=83°, and NO = 83 feet. Find the length of OP to the nearest tenth of a foot.

Answer 1

Since ∠P = 90º, ΔNOP is a right triangle which means we can use SOH-CAH-TOA [sin(angle)=opp/hyp, cos(angle)=adj/hyp, and tan(angle)=opp/adj] to find missing sides or missing angles.

After drawing and labeling the triangle, notice that NO is the hypotenuse. We know ∠N = 83° and we want to find the length of OP, which is the side that is opposite of ∠N. We can use sin(angle) = opp/hyp

sin(83º) = OP / 83ft *Plug in known values

83sin(83°) = OP *Solve for OP by multiplying both sides by 83

OP ≈ 82.4 ft *Plug into your calculator (make sure its in DEG mode, not RAD)

You could also use 83cos(7º) ≈ 82.4 ft

Answer 2

Draw and label a diagram!

OP / 83 = sin 83°

Can you solve for OP and answre?