Question

Solve for the right triangle.A=56° 41’, c= 253m, C=90°Draw the right triangle.Round side lengths to two decimal places if necessary.I believe they are looking for angle a, B and b since they have B, C and c.

Answer 1

Given the right triangle:

First, we know that ∡A and ∡B are complementary angles

$\begin{gathered} \measuredangle B=90\degree-\measuredangle A \\ \Rightarrow\measuredangle B=90\degree-56\degree41^{\prime} \\ \Rightarrow\measuredangle B=33\degree19^{\prime} \end{gathered}$

Now, using the trigonometric functions:

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

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

$\begin{gathered} \sin 56\degree41^{\prime}=\frac{a}{253}\Rightarrow a=211.42\text{ m} \\ \sin 33\degree19^{\prime}=\frac{b}{253}\Rightarrow b=138.96\text{ m} \end{gathered}$

Summarizing:

$\begin{gathered} \measuredangle A=33\degree19^{\prime} \\ a=211.42\text{ m} \\ b=138.96\text{ m} \end{gathered}$

: