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=(a)/(c) \\ \sin B=(b)/(c) \end{gathered}`

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

`\begin{gathered} \sin 56.3\degree=(a)/(2.2)\Rightarrow a=1.8\text{ mm} \\ \sin 33.7\degree=(b)/(2.2)\Rightarrow b=1.2\text{ mm} \end{gathered}`