Question

find x.
write your answer as an integer or as a decimal rounded to the nearest tenth.
x =
submit
work it out
not feeling ready yet? these can help:

Explanation:

Step1: Find the third angle

In a triangle, the sum of angles is \(180^{\circ}\). Let the third angle be \( \angle X\).
\(\angle V+\angle W+\angle X = 180^{\circ}\)
\(\angle V=180^{\circ}-(56^{\circ}+87^{\circ})=180^{\circ}-143^{\circ} = 37^{\circ}\)

Step2: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\)
Here, \(\frac{x}{\sin56^{\circ}}=\frac{6}{\sin87^{\circ}}\)
\(x=\frac{6\times\sin56^{\circ}}{\sin87^{\circ}}\)
Since \(\sin56^{\circ}\approx0.829\) and \(\sin87^{\circ}\approx0.998\)
\(x=\frac{6\times0.829}{0.998}=\frac{4.974}{0.998}\approx5.0\)

Answer:

\(x = 5.0\)