In ΔPQR, the measure of ∠R=90°, RQ = 80, PR = 39, and QP = 89. What is the value of the tangent of ∠Q to the nearest hundredth?

We have been given that in ΔPQR, the measure of ∠R=90°, RQ = 80, PR = 39, and QP = 89. We are asked to find the value of the tangent of ∠Q to the nearest hundredth.

First of all, we will draw a right triangle with our given information.

We know that tangent relates opposite side of right triangle with its adjacent side.  

We can see from our diagram that opposite side to angle Q is 39 and adjacent side to angle Q is 80.

Upon rounding to nearest hundredth, we will get:

Therefore, the value of tangent of Q is approximately 0.49 units.