Question

Pls help me I’ve been trying for the past ten minutes :)

Answer 1

We can easily find the value of angle B using the sine rule.

The sine rule is basically a ratio of the sides and sines of angles in a triangle.

It goes thus:

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

Where a, b, c and A, B, C are sides and opposite angles respectively.

We have a = 16, b = 10, A = 42 degrees, B = unknown.

Making B the subject of the formulae will lead us to cross multiply and get:

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

And B will be gotten by the sin inverse of the RHS. Mathematically, thus:

`B=\sin ^(-1)((b\sin A)/(a))`

Substituting, we get:

`\begin{gathered} B=\sin ^(-1)((10*\sin42)/(16)) \\ B=\sin ^(-1)0.4182 \\ B=24.72^o \end{gathered}`

B = 24.72 degrees