Solve by using the measurements ∠pqr = 90°, ∠qrp = 80°, and r = 15. round measures of sides to the nearest tenth and measures of angles to the nearest degree.

Part 1) The measure of angle ∠QPR=10°

Part 2) The measure of side q is q=15.2 units

Part 3) The measure of side p is p=2.6 units

Step-by-step explanation:

we know that

The triangle PQR is a right triangle

we have

∠PQR=90°

∠QRP=80°

∠QPR=?

r=15 units

q=?

p=?

step 1

Find the measure of angle ∠QPR

Remember that  

∠QRP+∠QPR=90° --------> by complementary angles

substitute the given value

80°+∠QPR=90°

∠QPR=90°-80°=10°

step 2

Find the length of the hypotenuse q (side PR)

we know that

The function sine of angle ∠QRP is equal to divide the opposite side to the angle ∠QRP (leg r side PQ) by the hypotenuse q (side PR)

sin(∠QRP)=PQ/PR

substitute the given values

sin(80°)=15/q

q=15/sin(80°)

q=15.2 units

step 3

Find the length of the leg p (side QR)

we know that

The function tangent of angle ∠QRP is equal to divide the opposite side to the angle ∠QRP (leg r side PQ) by the adjacent side to angle ∠QRP (leg p side QR)

tan(∠QRP)=PQ/QR

substitute the given values

tan(80°)=15/p

p=15/tan(80°)

p=2.6 units

see the attached figure to better understand the problem

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