Question

Find the missing lengths of the sides

a. A=9yd, c=18yd
b. A=9 yd, c=27yd
c. A=9sqrt3/2 9yd, c=9 sqrt 3yd
d. A=9 yd, c= 18 sqrt 3 yd

Answer 1

Your answer would be A.

according to the 30°, 60°, 90° triangle rules,
side a would equal x

`side \: b \: would \: equal \: x √(3)`
and side c would equal 2x

Answer 2

Option A is correct.

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.

`(a)/(sin\,A)=(b)/(sin\,B)=(c)/(sin\,C)`

`(a)/(sin\,30)=(9√(3))/(sin\,60)`

`a=(9√(3))/(sin\,60)* sin\,30`

`a=(9√(3))/((√(3))/(2))*(1)/(2)`

`a=18*(1)/(2)`

`a=9`

Now, Consider

`(9√(3))/(sin\,60)=(c)/(sin\,90)`

`c=(9√(3))/(sin\,60)* sin\,90`

`c=(9√(3))/((√(3))/(2))*1`

`c=18`

a = 9 yd and c = 18 yd

Therefore, Option A is correct.