Question

Can someone tell me the answer to this please this is mad confusing

Answer 1

12

Explanation:

Assume that those angles' curve in the triangle have same measure.

Law of Sin states that:

`\displaystyle \large{ ( \sin A)/(a) = ( \sin B)/(b) = ( \sin C)/(c) = 2R}`

From the question, assume that B and C are congruent or have same measure. Let B and C be congruent; angle B = angle C thus:-

`\displaystyle \large{ ( \sin B)/(b) = ( \sin C)/(c) } \\ \displaystyle \large{ ( \sin B)/(b) = ( \sin B)/(c) }`

Let b = x and c = 12; for angle B, it's not given so leave it.

`\ \displaystyle \large{ ( \sin B)/(x) = ( \sin B)/(12) }`

Multiply both sides by LCM which is 12x.

`\ \displaystyle \large{ ( \sin B)/(x)(12x) = ( \sin B)/(12)(12x) } \\ \ \displaystyle \large{12\sin B =\sin Bx }`

Divide both sides by sinB.

`\displaystyle \large{ (12\sin B)/(\sin B) = (\sin Bx )/( \sin B)} \\ \displaystyle \large{ 12 = x}`

Therefore, x = 12.