We are also given the following trigonometric expression.
cos y^(∘) = 5/13
Recall that in a right triangle, the cosine of an acute angle is defined as the ratio of the adjacent side to the hypotenuse.
cos θ = Adjacent/Hypotenuse
We will compare the given expression with this definition.
cos θ = Adjacent/Hypotenuse ⇒ cos y^(∘) = 5/13
Now, we can assume that the length of the adjacent side to y^(∘) is 5, and the length of the hypotenuse is 13.
Next, we will find the measure of x^(∘) by recalling the trigonometric ratio for sine.
sin θ = Opposite/Hypotenuse
Notice that this time, the side with length 5 is the opposite side to x^(∘) and the hypotenuse is 13.
We will rewrite the trigonometric ratio for sine by substituting these values.
sin θ = Opposite/Hypotenuse ⇒ sin x^(∘) = 5/13
To obtain the measure of x^(∘), we will apply the inverse sine into each side of this equation. Let's do it!
Now, we want to find the value of z by using the following equation.
x+2z = 7.1
To do so, we can substitute the value of x= 22.62 into this equation and solve it for z.
