Answer:
Option A is correct.
Step-by-step explanation:
Given:
Angles of the right angled triangle : 60° , 30° and 90°
Measurement of the side opposite to angle 60°, b is 9√3 yd
To find: Missing measures of the sides.
Vertex are marked and pic is attached.
We use Law of sines to find missing values.
[tex]\frac{a}{sin\,A}=\frac{b}{sin\,B}=\frac{c}{sin\,C}[/tex]
[tex]\frac{a}{sin\,30}=\frac{9\sqrt{3}}{sin\,60}[/tex]
[tex]a=\frac{9\sqrt{3}}{sin\,60}\times sin\,30[/tex]
[tex]a=\frac{9\sqrt{3}}{\frac{\sqrt{3}}{2}}\times\frac{1}{2}[/tex]
[tex]a=18\times\frac{1}{2}[/tex]
[tex]a=9[/tex]
Now, Consider
[tex]\frac{9\sqrt{3}}{sin\,60}=\frac{c}{sin\,90}[/tex]
[tex]c=\frac{9\sqrt{3}}{sin\,60}\times sin\,90[/tex]
[tex]c=\frac{9\sqrt{3}}{\frac{\sqrt{3}}{2}}\times1[/tex]
[tex]c=18[/tex]
a = 9 yd and c = 18 yd
Therefore, Option A is correct.
