Question

Match the ratio of side lengths to its corresponding anglemeasure.

Answer 1

Consider the formulae from Inverse Trigonometry,

`\begin{gathered} \theta=\sin ^(-1)(\frac{\text{ Opposite Leg}}{\text{ Hypotenuse}}) \\ \theta=\tan ^(-1)(\frac{\text{ Opposite Leg}}{\text{ Adjacent Leg}}) \\ \theta=\cos ^(-1)(\frac{\text{ Adjacent Leg}}{\text{ Hypotenuse}}) \end{gathered}`

Solve for the first angle as,

`\begin{gathered} \theta=\cos ^(-1)(0.139) \\ \theta\approx82^(\circ) \end{gathered}`

Thus, the required angle measure is 82 degrees approximately.

Solve for the second angle as,

`\begin{gathered} \theta=\tan ^(-1)(0.249) \\ \theta\approx14^(\circ) \end{gathered}`

Thus, the required angle measure is 14 degrees approximately.

Solve for the third angle as,

`\begin{gathered} \theta=\sin ^(-1)(0.469) \\ \theta\approx28^(\circ) \end{gathered}`

Thus, the required angle measure is 28degrees approximately.

Solve for the fourth angle as,

`\begin{gathered} \theta=\cos ^(-1)(0.682) \\ \theta\approx47^(\circ) \end{gathered}`

Thus, the required angle measure is 47 degrees approximately.

Solve for the fifth angle as,

`\begin{gathered} \theta=\sin ^(-1)(0.848) \\ \theta\approx58^(\circ) \end{gathered}`

Thus, the required angle measure is 58 degrees approximately.