Question

Abcd is a parallelogram. its diagonal, ac, is 18 inches long and forms a 20° angle with the base of the parallelogram. angle abc is 130°. what is the length of the parallelogram's base, ab?

Answer 1

Answer:

The length of base of parallelogram, AB = 11.75 in

Step-by-step explanation:

ABCD is a parallelogram. Its diagonal, AC, is 18 inches long and forms a 20° angle with the base of the parallelogram. Angle ABC is 130°

Please see attachment.

In ΔABC

  ∠A+∠B+∠C=180°           (Angle sum property of triangle)

20°+130°+∠C=180°         (∴ ∠A=20° , ∠B=130° )

                ∠C=30°

Using sine law:

$\dfrac{\sin C}{c}=\dfrac{\sin A}{a}=\dfrac{\sin B}{b}$

where, ∠C=30°, c=AB=? , b=18 , ∠B=130°

Substitute into formula

$\dfrac{\sin 30^\circ}{AB}=\dfrac{\sin 130^\circ}{18}$

$AB=\dfrac{18\cdot \sin 30^\cric}{\sin 130^\circ}$

$AB=\dfrac{18\cdot 0.5}{0.766}$

$AB=11.75\text{ in}$

Hence, The length of base of parallelogram, AB = 11.75 in

Answer 2

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