Question

Solve the right triangle.B= 33.7°, c= 2.2 mm, C = 90°Round to one decimal place.Draw the triangle.

Answer 1

Given the right triangle:

The angles ∡A and ∡B are complementary, then:

$\begin{gathered} \measuredangle A=90\degree^{}-\measuredangle B \\ \measuredangle A=90\degree^{}-33.7\degree \\ \measuredangle A=56.3\degree \end{gathered}$

Now, using the trigonometric functions:

$\begin{gathered} \sin A=\frac{a}{c} \\ \sin B=\frac{b}{c} \end{gathered}$

Then, using the values of A, B, and c to find a and b:

$\begin{gathered} \sin 56.3\degree=\frac{a}{2.2}\Rightarrow a=1.8\text{ mm} \\ \sin 33.7\degree=\frac{b}{2.2}\Rightarrow b=1.2\text{ mm} \end{gathered}$