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.

Question

asked Sep 20, 2021 202k views

2 Answers

GONG · Answer 1 · 2021-09-25T07:24:19+0000

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;

$\cos (Q)=(p^(2)+r^(2)-q^(2))/(2 p r)$

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

$\cos (Q)=(6^(2)+5^(2)-4^(2))/(2 (6)(5))$

Simplifying, we get;

$\cos (Q)=(36+25-16)/(2 (30))$

$\cos (Q)=(45)/(60)$

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.