Question

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.
Opposite side = 14 in.
Adjacent side = 22 in.
cos θ = ?

Answer 1

To find the value of cos θ, we need to use the given information of the opposite side and adjacent side.

Using the definition of cosine:

cos θ = adjacent side / hypotenuse

In this case, the adjacent side is 22 in and the hypotenuse is the missing value. We can find the hypotenuse using the Pythagorean theorem:

hypotenuse = sqrt((opposite side)^2 + (adjacent side)^2)
hypotenuse = sqrt((14 in)^2 + (22 in)^2)
hypotenuse ≈ 26.172 in (rounded to the nearest tenth)

Now, we can calculate cos θ:

cos θ = adjacent side / hypotenuse
cos θ = 22 in / 26.172 in
cos θ ≈ 0.8409 (rounded to four decimal places)