Practice Test - 12. Trigonometric Functions - McGraw Hill Glencoe Algebra 2, 2012

Let's analyze the given right triangle.

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 Concept:Right Triangle, we can use the Pythagorean Theorem 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}

SubstituteValues

Substitute values

9^{2} + b^{2} = 12^{2}

▼

Solve for

b

CalcPow

Calculate power

81 + b^{2} = 144

SubEqn

$LHS - 81 = RHS - 81$

b^{2} = 63

SqrtEqn

$LHS = RHS$

b = 63

UseCalc

Use a calculator

b = 7.937254 \dots

RoundDec

Round to $1$ decimal place(s)

b \approx 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 sine ratio.

Sine A = \frac{Opposite ∠ A}{H y p o t e n u s e} \Rightarrow sin A = \frac{a}{c}

By the definition of the inverse sine, the inverse sine of

\frac{9}{1 2}

is the measure of

∠ A .

To find it, we have to use a calculator.

m ∠ A = sin^{- 1} \frac{9}{1 2}

UseCalc

Use a calculator

m ∠ A = 48.590378 \dots

RoundInt

Round to nearest integer

m ∠ A \approx 4 9^{\circ}

What is more, according to the Rules:Interior Angles Theorem the sum of all angles in any given triangle is

18 0^{\circ} .

Therefore we can find

m ∠ B .

m ∠ A + m ∠ B + m ∠ C = 18 0^{\circ}

Let's substitute the given values and solve for

m ∠ B .

m ∠ A + m ∠ B + m ∠ C = 18 0^{\circ}

SubstituteII

$m ∠ A = 4 9^{\circ}$ , $m ∠ C = 9 0^{\circ}$

4 9^{\circ} + m ∠ B + 9 0^{\circ} = 18 0^{\circ}

▼

Solve for

m ∠ B

AddTerms

Add terms

13 9^{\circ} + m ∠ B = 18 0^{\circ}

SubEqn

$LHS - 13 9^{\circ} = RHS - 13 9^{\circ}$

m ∠ B = 4 1^{\circ}

Because

m ∠ A

was approximately

4 9^{\circ},

therefore the measure of angle

B

is also an approximation,

m ∠ B \approx 4 1^{\circ} .

Solved Triangle

Finally, let's gather all of our findings.

Exercise 4 Page 865

Hints

Check the answer

Practice exercises

Asses your skill

Side Length

Angle Measures

Solved Triangle