Determine the trigonometric ratio to use according to the given information and the unknown.
x = 21.9, y = 20.8
Practice makes perfect
We are given the length of the hypotenuse and the measure of an acute angle of a right triangle. We will find values of x and y one at a time.
Value of x
x is a length of the side opposite to the given angle.
Note that the given side is the hypotenuse, and the side we want to find is opposite to the given angle. Therefore, we will use the sine ratio.
sin θ = opposite/hypotenuse
In our triangle, we have that θ = 46.5^(∘) and the length of the hypotenuse is 30.2. We want to find the length of the leg opposite to the angle.
y is a length of the side adjacent to the given angle.
As we can see, the given side is the hypotenuse, and the side we want to find is adjacent to the given angle. This means that we will use the cosine ratio.
cos θ = adjacent/hypotenuse
Similar as before, we have that θ = 46.5^(∘) and the length of the hypotenuse is 30.2. Let's find the length of the leg adjacent to the angle.
