Question

What is the length of side q, given r = 20, s = 30, and Q = 15°? Round the answer to the nearest tenth. mc022-1.jpg [Not drawn to scale] 11.9 40.7 140.9 1659.1

Answer 1

Option a)

11.9 is correct answer.

Explanation:

Given that in a triangle QRS, we have side r =20, s=30 and Q= 15 degrees

We have to find the side length q.

Use cosine formula for triangles.

`q^2=r^2+s^2-2rs cos Q\\     = 20^2+30^2-2(600)cos 15\\     =1300-1159.11\\    q = 11.911`

Round off to one decimal.

q = 11.9

Answer 2

The smallest angle in the triangle must be opposite the shortest side. The only viable answer among the choices offered is the one that is less than 20. (In no event can side q be longer than 20+30=50.)

The appropriate choice is
11.9