Question

The two non-parallel sides of an isosceles trapezoid are each 7 feet long. the longer of the 2 bases measures 22 feet. the sun of the base angles is 140 degrees.

Use the Law of Cosines to find the length of the diagonal.
Use the Law of Sines to find the length of the shorter base

Answer 1

formula:

c^2 = a^2 + b^2 - 2abcos(C)

where c is the length of the diagonal, a and b are the lengths of the legs of the triangle (the non-parallel sides of the trapezoid), and C is the angle between them.

In this case, a = b = 7 feet and C = (180 - 140)/2 = 20 degrees. We can plug these values into the formula to find:

c^2 = 7^2 + 7^2 - 2(7)(7)cos(20)

c = sqrt(98 + 49cos(20))

To use the Law of Sines to find the length of the shorter base, we can use the following formula:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the sides of the triangle and A, B, and C are the angles opposite those sides.

Since we know a and b, we can use the formula to find:

x/sin(140) = 7/sin(20)

x = 7sin(140) / sin(20)

Note that the value of c will be in squared units, so you need to take the square root to get the actual length of the diagonal.