Using Trig Ratios

Which of the following is the correct ratio to solve for x?

¿Cuál de las siguientes es la razón correcta para encontrar x?

• $\sin56\degree=\frac{20}{x}$

• $\sin56\degree=\frac{x}{20}$
  

• $\cos56\degree\equiv\frac{20}{x}$
  

• $\cos56\degree=\frac{x}{20}$
  

Answer explanation

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

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

Which of the following is the correct ratio to solve for x?

¿Cuál de las siguientes es la razón correcta para encontrar x?

• $\sin18\degree=\frac{x}{20}$
  

• $\sin18\degree=\frac{20}{x}$
  

• $\cos18\degree=\frac{20}{x}$
  

• $\cos18\degree=\frac{x}{20}$
  

Answer explanation

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

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

Which of the following is the correct ratio to solve for x?

¿Cuál de las siguientes es la razón correcta para encontrar x?

• $\tan60\degree=\frac{18}{x}$

• $\tan60\degree=\frac{x}{18}$

• $\sin60\degree=\frac{x}{18}$
  

• $\cos60\degree=\frac{18}{x}$
  

Answer explanation

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

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

Solve for x. Round to the nearest tenth.

Make sure your calculator is in DEGREE mode.

• 74.9

• 3.6

• 63.5

• 54.1

Answer explanation

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

Solve for x. Round to the nearest tenth.

Make sure your calculator is in DEGREE mode.

• 11.1

• 9.3

• 13.0

• 5.5

Answer explanation

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

Solve for x. Round to the nearest tenth.

Make sure your calculator is in DEGREE mode.

• 28.7

• 3.3

• 53.3

• 43.5

Answer explanation

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

Solve for x. Round to the nearest tenth.

Make sure your calculator is in DEGREE mode.

• 25.7

• 35.4

• 6.4

• 5.6

Answer explanation

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

Solve for x. Round to the nearest tenth.

Make sure your calculator is in DEGREE mode.

• 5.0

• 32.2

• 3.8

• 5.3

Answer explanation

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

Solve for x. Round to the nearest tenth.

Make sure your calculator is in DEGREE mode.

• 40.7

• 44.6

• 48.8

• 8.9

Answer explanation

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

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.

• True

• False

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.