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:
[tex]\dfrac{\sin C}{c}=\dfrac{\sin A}{a}=\dfrac{\sin B}{b}[/tex]
where, ∠C=30°, c=AB=? , b=18 , ∠B=130°
Substitute into formula
[tex]\dfrac{\sin 30^\circ}{AB}=\dfrac{\sin 130^\circ}{18}[/tex]
[tex]AB=\dfrac{18\cdot \sin 30^\cric}{\sin 130^\circ}[/tex]
[tex]AB=\dfrac{18\cdot 0.5}{0.766}[/tex]
[tex]AB=11.75\text{ in}[/tex]
Hence, The length of base of parallelogram, AB = 11.75 in
