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

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

`\begin{gathered} \sin 56\degree41^(\prime)=(a)/(253)\Rightarrow a=211.42\text{ m} \\ \sin 33\degree19^(\prime)=(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}`

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