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.
θ = 43°
Adjacent side = 109 ft
Hypotenuse = ?
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.
To find the missing value of the right triangle, we can use the cosine function, since we know the adjacent side and the angle.
We have the following information:
Angle: θ = 43°
Adjacent side: Adjacent = 109 ft
Using the cosine function:
cos(θ) = Adjacent / Hypotenuse
Plugging in the given values, we get:
cos(43°) = 109 ft / Hypotenuse
Now, let's solve for the hypotenuse (H):
Hypotenuse = Adjacent / cos(θ)
Substituting the given values:
Hypotenuse = 109 ft / cos(43°)
Now, let's calculate the hypotenuse:
Hypotenuse = 109 ft / cos(43°)
Hypotenuse ≈ 154.46 ft
Rounding the hypotenuse to the nearest tenth, the missing value is approximately 154.5 ft.