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°

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 &=(225+169-289)/(390) \\\cos C &=(105)/(390) \\\cos C & \approx 0.26923 \\C & \approx \cos (0.26923) \\C & \approx 74^(\circ)\end{aligned}$$`