Let's analyze the given .
We will find the missing measures one at a time. In this case, this means that we want to find m ∠A, m∠B, and b.
Side Length
Knowing two sides of a , we can use the to find the remaining one.
a^2 + b^2 = c^2
Let's substitute the given values and solve for b.
a^2 + b^2 = c^2
9^2 + b^2 = 12^2
81 + b^2 = 144
b^2 = 63
b = sqrt(63)
b = 7.937254...
b ≈ 7.9
Since the length of the side of the triangle cannot be negative, we only consider the positive solution.
Angle Measures
We can find m ∠A using a ratio.
Sine A=Opposite ∠A/Hypotenuse ⇒ sin A = a/c
By the definition of the , the inverse sine of 912 is the measure of ∠A. To find it, we have to use a calculator.
m ∠A = sin^(- 1) 9/12
m ∠A = 48.590378...
m ∠A ≈ 49^(∘)
What is more, according to the the sum of all angles in any given triangle is 180^(∘). Therefore we can find m ∠B.
m ∠A + m∠B + m ∠C = 180^(∘)
Let's substitute the given values and solve for m ∠B.
m ∠A + m ∠B + m ∠C = 180^(∘)
49 ^(∘) + m ∠B + 90^(∘) = 180^(∘)
139^(∘) + m ∠B = 180^(∘)
m ∠B = 41^(∘)
Because m ∠A was approximately 49^(∘), therefore the measure of angle B is also an approximation, m ∠B ≈ 41^(∘).
Solved Triangle
Finally, let's gather all of our findings.
