Question

In trapazoid abcd ab is parallel to dc, bc is perpendicular to dc determine the measure of d to the nearest degree and find the lemgth of ad in simplest radicial form

Answer 1

∠d = 56.3°

AD = 3.6 inches

Step-by-step explanation:

The trapezoid can be decompose to a rectangle and a triangle. The triangle has a hypotenuse AD, height of 3 inches and base of 2 inches (7 - 5)

`tan(d)=(opposite)/(adjacent) =(height)/(base) \\tan(d)=(3)/(2) \\tan(d)=1.5\\d=tan^(-1)(1.5)=56.3^0`

Therefore, ∠d = 56.3°

Using Pythagorean theorem:

AD² = base² + height²

AD² = 3² + 2²

AD² = 9 + 4 = 13

AD = √13 = 3.6 inches