Question

Find a.Round to the nearest tenth:2 cmс1501050a=a = [ ? ]cmLaw of Sines: sin A=sin Bb=sin Cсa

Answer 1

In the given triangle ABC ,

Sum of the angles of of a triangle is 180 degrees.

Therefore,

`\begin{gathered} \angle A\text{ + }\angle B\text{ + }\angle C\text{ = 180} \\ \angle A\text{ + 105 + 15 = 180} \\ \angle A=\text{ 180 - 120} \\ \angle A\text{ = 60} \end{gathered}`

By using sine rule,

`(a)/(\sin A)\text{ = }(b)/(\sin B)`

Substituting the given values in the given equation,

`\begin{gathered} (a)/(\sin60)\text{ = }(2)/(\sin 105) \\ a\text{ = }(2\sin 60)/(\sin 105) \\ a\text{ = 1.7931 } \\ a\text{ }\approx\text{ 1.8 }cm \end{gathered}`