Question

The sides of a triangle are 17 ft, 19 ft, and 15 ft. Find the measure of the angle opposite the longest side. Round your answer to the nearest degree.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the measure of the angle opposite the longest side, we can use the Law of Cosines. The formula is as follows:

c^2 = a^2 + b^2 - 2ab * cos(C)

where c is the length of the longest side (19 ft in this case), a and b are the lengths of the other two sides (17 ft and 15 ft), and C is the angle opposite the longest side that we want to find.

Plugging in the values we have:

19^2 = 17^2 + 15^2 - 2 * 17 * 15 * cos(C)
361 = 289 + 225 - 510cos(C)
361 = 514 - 510cos(C)
-153 = -510cos(C)
cos(C) = 0.3

Now we can find the angle C by taking the arccosine of 0.3:

C = arccos(0.3) ≈ 72.53 degrees

Therefore, the measure of the angle opposite the longest side is approximately 73 degrees.