In ΔQRS, q = 91 inches, r = 67 inches and ∠S=109°. Find the length of s, to the nearest inch.

The length of s is 129 inches to the nearest inch.

Step-by-step explanation:

In ΔQRS

∵ q is the side that opposite of ∠Q

∵ r is the side that opposite of ∠R

∵ s is the side that opposite of ∠S

∵ q = 91 inches, r = 67 inches, m∠S = 109°

→ To find side s we will use the cosine rule

∵ s² = q² + r² - 2(q)(r)cos∠S

∴ s² = (91)² + (67)² - 2(91)(67)cos(109°)

∴ s² = 16739.97808

→ Take square root for both sides

∴ s = 129.3830672

→ Round it to the nearest inch (whole number)

∴ s = 129 inches

∴ The length of s is 129 inches to the nearest inch.

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