Final answer:
To find the length of q in a given triangle, we use the cosine rule and substitute the given values to solve for q.
Step-by-step explanation:
In the given triangle ΔQRS, we are given that r = 83 cm, ∠R = 161°, and ∠S = 5°. We need to find the length of q, rounded to the nearest centimeter.
To find the length of q, we can use the cosine rule, which states that c^2 = a^2 + b^2 - 2ab * cos(C), where c is the side opposite to angle C.
Using the cosine rule, we have:
q^2 = r^2 + s^2 - 2rs * cos(RS)
Substituting the given values into the formula, we get:
q^2 = 83^2 + s^2 - 2 * 83 * s * cos(5°)
Simplifying the equation and solving for q, we find that q ≈ 83 cm.