Applying Trigonometric Functions - High School Math

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Question

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

Answer

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

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

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

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Question

In this figure, if angle $c=90^\circ$ , side , and side , what is the measure of angle ?

Answer

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

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

In this problem, that would be:

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

Plug in our given values:

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

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

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

$a=41.8^\circ$

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Question

In this figure, side , , and $c=90^\circ$ . What is the value of angle ?

Answer

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

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

In this problem, that would be:

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

Plug in our given values:

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

$\cos(a)=0.65$

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

$a=49.46^\circ$

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