Mathematics: 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

Find the missing lengths of the sides a. a=9yd, c=18yd

perezesmeralda78

13.03.2022

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.

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