Question

the sides of a triangle are 15 ft, 17 ft, and 13 ft. find the measure of the angle opposite the longest side. round your answer to the nearest degree

Answer 1

Answer: 74°

Step-by-step explanation:

$Using the Law of Cosines: \begin{aligned} \text { Given, } a &=15 f t, \ b=13 f t, \ c=17 f t \\c^{2} &=a^{2}+b^{2}-2 a b \cos C \\(17)^{2} &=(15)^{2}+(13)^{2}-2(15)(13) \cos C \\289 &=225+169-390 \cos C \\390 \cos C &=225+169-289 \\\cos C &=\frac{225+169-289}{390} \\\cos C &=\frac{105}{390} \\\cos C & \approx 0.26923 \\C & \approx \cos (0.26923) \\C & \approx 74^{\circ}\end{aligned}$