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 = ?
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)
To solve for the missing value of the right triangle, we can use the given values of the opposite side and adjacent side.
Given:
Opposite side (O) = 14 in
Adjacent side (A) = 22 in
To find the missing value, we can use the cosine function:
cos θ = A / H
Where:
θ is the angle
A is the adjacent side
H is the hypotenuse
In this case, we need to find cos θ, so we'll rearrange the formula to solve for it.
cos θ = A / H
Since H is the hypotenuse, we need to use the Pythagorean theorem to find its value.
Pythagorean theorem:
H^2 = A^2 + O^2
Substituting in the given values:
H^2 = 22^2 + 14^2
H^2 = 484 + 196
H^2 = 680
H = sqrt(680)
H ≈ 26.077
Now we have all the values to calculate cos θ:
cos θ = A / H
cos θ = 22 / 26.077
cos θ ≈ 0.8448
Therefore, cos θ ≈ 0.8448.