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High School Math : Applying Trigonometric Functions

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Example Questions

Example Question #1 : Triangles

Rt_triangle_letters In this figure, side X=20 $\displaystyle X=20$, Y=13 $\displaystyle Y=13$, and $c=90^\circ$ $\displaystyle c=90^\circ$. What is the value of angle $\displaystyle a$?

Possible Answers:

$40.54^\circ$ $\displaystyle 40.54^\circ$

Undefined

$6.5^\circ$ $\displaystyle 6.5^\circ$

$90^\circ$ $\displaystyle 90^\circ$

$49.46^\circ$ $\displaystyle 49.46^\circ$

Correct answer:

$49.46^\circ$ $\displaystyle 49.46^\circ$

Explanation:

Since $c=90^\circ$ $\displaystyle c=90^\circ$, we know we are working with a right triangle.

That means that $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$ $\displaystyle \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$.

In this problem, that would be:

$\cos(a)=\frac{\text{Y}}{\text{X}}$ $\displaystyle \cos(a)=\frac{\text{Y}}{\text{X}}$

Plug in our given values:

$\cos(a)=\frac{\text{13}}{\text{20}}$ $\displaystyle \cos(a)=\frac{\text{13}}{\text{20}}$

$\cos(a)=0.65$ $\displaystyle \cos(a)=0.65$

$a=\cos^{-1}(0.65)$ $\displaystyle a=\cos^{-1}(0.65)$

$a=49.46^\circ$ $\displaystyle a=49.46^\circ$

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Example Question #1 : Right Triangles

Let ABC be a right triangle with sides $\displaystyle A$ = 3 inches, $\displaystyle B$ = 4 inches, and $\displaystyle C$ = 5 inches. In degrees, what is the $\sin \Theta$ $\displaystyle \sin \Theta$ where $\Theta$ $\displaystyle \Theta$ is the angle opposite of side $\displaystyle A$?

Possible Answers:

$\displaystyle .3$

$\displaystyle .5$

$\displaystyle .6$

$\displaystyle .7$

$\displaystyle .4$

Correct answer:

$\displaystyle .6$

Explanation:

3-4-5_triangle

We are looking for $\sin(\theta )$ $\displaystyle \sin(\theta )$. Remember the definition of sin $\displaystyle sin$ in a right triangle is the length of the opposite side divided by the length of the hypotenuse.

So therefore, without figuring out $\Theta$ $\displaystyle \Theta$ we can find

$\sin \Theta =\frac{3}{5}=.6$ $\displaystyle \sin \Theta =\frac{3}{5}=.6$

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Example Question #1 : Trigonometric Functions

Rt_triangle_letters

In this figure, if angle $c=90^\circ$ $\displaystyle c=90^\circ$, side X=12 $\displaystyle X=12$, and side Z=8 $\displaystyle Z=8$, what is the measure of angle $\displaystyle a$?

Possible Answers:

$41.8^\circ$ $\displaystyle 41.8^\circ$

$90^\circ$ $\displaystyle 90^\circ$

$\frac{2}{3}^\circ$ $\displaystyle \frac{2}{3}^\circ$

$48.2^\circ$ $\displaystyle 48.2^\circ$

Undefined

Correct answer:

$41.8^\circ$ $\displaystyle 41.8^\circ$

Explanation:

Since $c=90^\circ$ $\displaystyle c=90^\circ$, we know we are working with a right triangle.

That means that $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$ $\displaystyle \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$.

In this problem, that would be:

$\sin(a)=\frac{\text{Z}}{\text{X}}$ $\displaystyle \sin(a)=\frac{\text{Z}}{\text{X}}$

Plug in our given values:

$\sin(a)=\frac{8}{12}$ $\displaystyle \sin(a)=\frac{8}{12}$

$\sin(a)=\frac{2}{3}$ $\displaystyle \sin(a)=\frac{2}{3}$

$a=\sin^{-1}(\frac{2}{3})$ $\displaystyle a=\sin^{-1}(\frac{2}{3})$

$a=41.8^\circ$ $\displaystyle a=41.8^\circ$

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High School Math : Applying Trigonometric Functions

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Triangles

Example Question #1 : Right Triangles

Example Question #1 : Trigonometric Functions

All High School Math Resources

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DMCA Complaint

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