Think about a right triangle where you are given all of the side lengths.
See solution.
Practice makes perfect
Let's imagine that one the rooms of our house is in the shape of a right triangle. We want to find its angle measures to design a special carpet for the room.
With all of the side lengths, we can find the corresponding angles one at a time. To do so, we will start by recalling the Law of Cosines.
a^2= b^2+ c^2-2 b c * cos A
b^2= a^2+ c^2-2 a c * cos B
c^2= a^2+ b^2-2 a c * cos CLet's use the first formula to find the value of m ∠A. We will substitute a= 4, b= 5, and c= 3 into the formula.
Then we need to use inverse cosine to isolate the measure of the angle.
cos A=3/5 ⇔ m ∠A=cos^(-1)(3/5)
To do so we will use a calculator. We need to first push MODE in our calculator and change Radian to Degree.
Then, we push 2ND followed by COS, introduce the value 35, and push ENTER.
The inverse cosine of 35 is about 53^(∘), which corresponds to the value of m ∠A. With this value we can find the third angle measure B. Let's use the Triangle Angle Sum Theorem.
53 ^(∘) + 90 ^(∘) + m ∠C = 180 ^(∘)
⇓
m ∠C ≈ 37 ^(∘)
Great! Now, we can complete our right triangle.
