Question

Find the missing lengths of the sides

Answer 1

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.

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

$\frac{a}{sin\,30}=\frac{9\sqrt{3}}{sin\,60}$

$a=\frac{9\sqrt{3}}{sin\,60}\times sin\,30$

$a=\frac{9\sqrt{3}}{\frac{\sqrt{3}}{2}}\times\frac{1}{2}$

$a=18\times\frac{1}{2}$

$a=9$

Now, Consider

$\frac{9\sqrt{3}}{sin\,60}=\frac{c}{sin\,90}$

$c=\frac{9\sqrt{3}}{sin\,60}\times sin\,90$

$c=\frac{9\sqrt{3}}{\frac{\sqrt{3}}{2}}\times1$

$c=18$

a = 9 yd and c = 18 yd

Therefore, Option A is correct.

Answer 2

Your answer would be A.

according to the 30°, 60°, 90° triangle rules,
side a would equal x
$side \: b \: would \: equal \: x \sqrt{3}$
and side c would equal 2x