Answer:
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
