Question

A piece of wire 6.2 ft. long is bent into a triangular shape. One side is 1.7 ft. long and another is 2.4 ft. long. Find the angles of the triangle.

Answer 1

To find the angles of the triangle, subtract the sum of the two known sides from the total length to get the third side. Then use the Law of Cosines to calculate each angle by applying the formula for cosine of an angle in terms of the sides of a triangle. Finally, confirm the angles sum up to 180 degrees.

Step-by-step explanation:

To find the angles of the triangle formed from a 6.2 ft. length of wire with sides measuring 1.7 ft., 2.4 ft., and the remaining side is the difference of 6.2 ft. minus the sum of 1.7 ft. and 2.4 ft., you can use the Law of Cosines. First, calculate the length of the third side:

Third side = Total length - (First side + Second side)
= 6.2 ft. - (1.7 ft. + 2.4 ft.)
= 6.2 ft. - 4.1 ft.
= 2.1 ft.

Now, apply the Law of Cosines to find each angle:

For the angle opposite the first side (1.7 ft.):

Cosine(angle) = (2.4^2 + 2.1^2 - 1.7^2) / (2 * 2.4 * 2.1)

For the angle opposite the second side (2.4 ft.):

Cosine(angle) = (1.7^2 + 2.1^2 - 2.4^2) / (2 * 1.7 * 2.1)

For the angle opposite the third side (2.1 ft.):

Cosine(angle) = (1.7^2 + 2.4^2 - 2.1^2) / (2 * 1.7 * 2.4)

Calculate the cosines and then use the arccos function to find the angle measures in degrees. Add all angles together to check if they sum to 180 degrees, confirming that the triangle is valid.