Notice that the given triangle is isosceles. What does it say about its angles and side lengths?
x≈ 18.8, y≈ 25.9
Practice makes perfect
Consider the given triangle.
Note that the two sides of the triangle are congruent. Therefore, both of them have the length of 32 and the triangle is isosceles. Also, both angles near the base of the triangle have equal measures. Let's add this information to our diagram.
We want to find the values of x and y. To do that we will consider the smaller triangle, which is a right triangle. Let's find the variables one at a time.
Finding x
Let's take a look at the right triangle.
Note that the given side is the hypotenuse of the triangle, and the side we want to find is adjacent to the given angle. Therefore, we will use the cosine ratio.
cos θ = Length of leg adjacent toθ/Length of hypotenuse
In our triangle, we have that θ =54^(∘) and the length of the hypotenuse is 32. We want to find the length of the leg adjacent to the angle.
Let's add the obtained information to the diagram.
We know the length of the hypotenuse and this time we want to find the length of the side opposite to the given angle. Therefore, we will use the sine ratio.
sin θ = Length of leg opposite toθ/Length of hypotenuse
In our triangle, we have that θ =54^(∘) and the length of the hypotenuse is 32. We want to find the length of the leg opposite to the angle.
