Question

solve the right triangle.
round your answers to the nearest tenth.

\\(a = 66^{\circ}\\)
\\(a = \\)
\\(b = \\)

Explanation:

Find the unknown angle \(A\)

Using the Solving Right Triangles knowledge point

$$ A = 90^\circ - 46^\circ = 44^\circ $$

Set up trigonometric ratios for side \(a\)

Using the Right Triangle Trigonometry knowledge point

$$ \cos(46^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{a}{24} $$

Calculate the length of side \(a\)

Using the Solving Right Triangles knowledge point

$$
LATEXBLOCK0
$$

Set up trigonometric ratios for side \(b\)

Using the Right Triangle Trigonometry knowledge point

$$ \sin(46^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{b}{24} $$

Calculate the length of side \(b\)

Using the Solving Right Triangles knowledge point

$$
LATEXBLOCK1
$$

Answer:

Solve the right triangle. Round your answers to the nearest tenth.

\(A = 66^\circ\) (Note: The image shows a pre-filled value of \(A = 66^\circ\), but mathematically the acute angles of a right triangle must sum to \(90^\circ\). Since the given angle is \(46^\circ\), the correct mathematical value for \(A\) is \(90^\circ - 46^\circ = 44^\circ\). Below are the calculated side lengths based on the geometric diagram where the hypotenuse is 24 and the adjacent angle to side \(a\) is \(46^\circ\).)

\(a =\) <blank>16.7</blank>
\(b =\) <blank>17.3</blank>