Question

c. a right triangle with an angle of \\(58^\circ\\), adjacent side of \\(40\text{ in.}\\), and hypotenuse labeled \\(x\\).
d. a right triangle with an angle of \\(73^\circ\\), opposite side of \\(8\text{ m}\\), and adjacent side labeled \\(x\\).

Explanation:

Set up trigonometric ratio for part c

Using the Right Triangle Trigonometry knowledge point

$$ \cos(58^\circ) = \frac{40}{x} $$

Solve for x in part c

Using the Solving Right Triangles knowledge point

$$ x = \frac{40}{\cos(58^\circ)} \approx \frac{40}{0.5299} \approx 75.5\text{ in.} $$

Set up trigonometric ratio for part d

Using the Right Triangle Trigonometry knowledge point

$$ \tan(73^\circ) = \frac{8}{x} $$

Solve for x in part d

Using the Solving Right Triangles knowledge point

$$ x = \frac{8}{\tan(73^\circ)} \approx \frac{8}{3.2709} \approx 2.4\text{ m} $$

Answer:

Question c

\(x \approx 75.5\text{ in.}\)

Question d

\(x \approx 2.4\text{ m}\)