Using Trig Ratios

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Answer explanation

$\sin\theta=\frac{opposite}{hypotenuse}$

$\sin56\degree=\frac{x}{20}$

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Answer explanation

$\cos\theta=\frac{adjacent}{hypotenuse}$

$\cos18\degree=\frac{20}{x}$

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Answer explanation

$\tan\theta=\frac{opposite}{adjacent}$

$\tan60\degree=\frac{18}{x}$

Front

Solve for x. Round to the nearest tenth. Make sure your calculator is in DEGREE mode.

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54.1

Answer explanation

$\sin15\degree=\frac{opposite}{hypotenuse}=\frac{14}{x}$
Switch $\sin15\degree$ with $x$ .
$x=\frac{14}{\sin15\degree}\approx54.1$

Front

Solve for x. Round to the nearest tenth. Make sure your calculator is in DEGREE mode.

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9.3

Answer explanation

$\cos32\degree=\frac{adjacent}{hypotenuse}=\frac{x}{11}$
$11\cdot\cos32\degree=x$
$x\approx9.3$

Front

Solve for x. Round to the nearest tenth. Make sure your calculator is in DEGREE mode.

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43.5

Answer explanation

$\sin16\degree=\frac{opposite}{hypotenuse}=\frac{12}{x}$
Switch $\sin16\degree$ with $x.$
$x=\frac{12}{\sin16\degree}\approx43.5$

Front

Solve for x. Round to the nearest tenth. Make sure your calculator is in DEGREE mode.

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5.6

Answer explanation

$\tan65\degree=\frac{opposite}{adjacent}=\frac{12}{x}$
Switch $\tan65\degree$ with $x.$
$x=\frac{12}{\tan65\degree}\approx5.6$

Front

Solve for x. Round to the nearest tenth. Make sure your calculator is in DEGREE mode.

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3.8

Answer explanation

$\cos70\degree=\frac{adjacent}{hypotenuse}=\frac{x}{11}$
$11\cdot\cos70\degree=x\approx3.8$

Front

Solve for x. Round to the nearest tenth. Make sure your calculator is in DEGREE mode.

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40.7

Answer explanation

$\tan65\degree=\frac{opposite}{adjacent}=\frac{x}{19}$
$19\cdot\tan65\degree=x\approx40.7$

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True or false: If we only know the length of one side of the right triangle and the measure of an angle we can use Trigonometry to find the lengths of the other two sides.

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True

Answer explanation

True. We can use an angle measure and side length to find a missing side by using the sine, cosine, or tangent ratio.