Solving Triangles Using Trigonometry

Front

What is the measurement of the unknown angle if the opposite side is 28 and the adjacent side is 21?

Back

Use the tangent function: \( \tan^{-1}\left(\frac{28}{21}\right) \approx 55.2° \) (rounded to the nearest tenth).

Front

What is the correct equation to solve for the missing side when given an angle of 40° and hypotenuse of 28?

Back

The correct equation is \( \sin 40 = \frac{w}{28} \).

Front

What does the acronym SOH CAH TOA stand for in trigonometry?

Back

SOH: Sine = Opposite/Hypotenuse, CAH: Cosine = Adjacent/Hypotenuse, TOA: Tangent = Opposite/Adjacent.

Front

Solve for x if \( \sin 30 = \frac{x}{10} \).

Back

\( x = 10 \cdot \sin 30 = 5 \).

Front

What is the correct equation to solve for x if \( \tan 58 = \frac{11}{x} \)?

Back

Rearranging gives \( x = \frac{11}{\tan 58} \).

Front

What is the sine of an angle in a right triangle?

Back

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

Front

What is the cosine of an angle in a right triangle?

Back

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

What is the tangent of an angle in a right triangle?

Back

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

Front

If the opposite side is 5 and the adjacent side is 12, what is the angle using tangent?

Back

\( \tan^{-1}\left(\frac{5}{12}\right) \approx 22.6° \) (rounded to the nearest tenth).

Front

What is the relationship between the sides and angles in a right triangle?

Back

The angles in a right triangle determine the ratios of the lengths of the sides, which can be solved using trigonometric functions.