Question

30 POINTS HELP ANSWER ASAP AND EXPLAIN STEP BY STEP HOW TO SOLVE The two non-parallel sides of an isosceles trapezoid are each 7 feet long. The longer of the two bases measures 22 feet long. The sum of the base angles is 140°.
a.
Find the length of the diagonal.
b.
Find the length of the shorter base.

Round your answers to the nearest hundredth.

Answer 1

Cosine (70°) = x / 7
x = cosine (70°) * 7
x = 0.34202 * 7
x = y = 2.39414
Short Base = 22 - 2*(2.39414)
Short Base = 17.21172

Diagonal² = (17.21172 + 2.39414)² + (6.57785)²

Diagonal² = (19.60586)² +  43.2681106225

Diagonal² = 384.3897463396 + 43.2681106225

Diagonal² = 427.6578569621

Diagonal = 20.6798901584

Answer 2

See diagram
I wrote that the degrees are 70 each because it is isocolese and 140/2=70


a.
to solve for the diagonal, I'm going to use trig to find the height and the base then use pythagorean theorem to find the diagonal

so
see I've drawn an auxiliry line to make a right triangle on the leftmost side
so
we want to find the height and base
sin(70°)=h/7
so 7sin(70°)=h≈6.57785

cos(70°)=base/7
so 7cos(70°)=base≈2.39414

now
the entire long base is 22, so that big triangle with the diagonal as the hyptonuse is 22-2.39414=19.6059
use pythagorean theorem, like 6.57785²+19.6059²=diagonal²
we get that the diagonal is about 20.68ft




b.
we got that the base was 7cos(70°)
2 of those bases so 22-14cos(70°)=17.2117ft or rounded 17.21ft




a. 20.68ft
b. 17.21ft