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.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
We can see from our diagram that opposite side to angle Q is 39 and adjacent side to angle Q is 80.
[tex]\text{tan}(Q)=\frac{39}{80}[/tex]
[tex]\text{tan}(Q)=0.4875[/tex]
Upon rounding to nearest hundredth, we will get:
[tex]\text{tan}(Q)\approx 0.49[/tex]
Therefore, the value of tangent of Q is approximately 0.49 units.
