Using the info given, solve for the missing value of the right triangle. Round each angle to the nearest degree, each length to the nearest tenth, & each trigonometric value to four decimal places, if necessary.

Question

θ = 43°
Adjacent side = 109 ft
Hypotenuse = ?

Answer 1

To find the missing value of the right triangle, we can use the trigonometric ratio cosine (cos).

In this case, the adjacent side is given as 109 ft, and the angle θ is given as 43°. We want to find the length of the hypotenuse.

Using the cosine ratio:
cos(θ) = adjacent/hypotenuse

Plugging in the values we know:
cos(43°) = 109 ft/hypotenuse

To solve for the hypotenuse, we rearrange the equation:
hypotenuse = 109 ft / cos(43°)

Calculating the value:
hypotenuse ≈ 151.346 ft

Therefore, the approximate length of the hypotenuse is 151.3 ft.