Question

Find the measure of Q, the smallest angle in the triangle whose sides have lengths 4-5, and 6. Round the measure to the nearest whole degree.

Answer 1

Given:

Given that PQR is a triangle.

The measures of the sides of the triangle are 4,5 and 6.

We need to determine the measure of ∠Q.

Measure of ∠Q:

The measure of ∠Q can be determined using the law of cosines formula.

Thus, we have;

$\cos (Q)=\frac{p^{2}+r^{2}-q^{2}}{2 p r}$

Substituting p = 6, q = 4, r = 5, we get;

$\cos (Q)=\frac{6^{2}+5^{2}-4^{2}}{2 (6)(5)}$

Simplifying, we get;

$\cos (Q)=\frac{36+25-16}{2 (30)}$

$\cos (Q)=\frac{45}{60}$

Dividing, we get;

$\cos (Q)=0.75$

      $Q=cos^{-1}(0.75)$

      $Q=41^{\circ}$

Thus, the measure of ∠Q is 41°

Hence, Option b is the correct answer.