In the diagram, we are given that the area of sector RSQ is 27.93 square feet. The central angle m∠ RSQ is 50^(∘).
We first need to calculate the measure of the minor arc, mRQ. Recalling that the measure of an arc equals its corresponding central angle, we can identify mRQ as follows.
m∠RSQ=50^(∘) ⇔ mRQ= 50^(∘)
We can now find the measure of the major arc mRTQ by subtracting mRQ to 360^(∘).
mRTQ=360^(∘)- 50^(∘) ⇔ mRTQ= 310^(∘)
To find the area of the sector RTQ we also need the value of r or r^2. To do so, let's substitute A= 27.93 and mRQ= 50 in the formula of the area of a sector and solve of r^2
