ACT Practice - Trigonometry

In a 3-4-5 right triangle, what is the sine of the smallest angle?

• 
  

  $\frac{3}{4}$
  

• $\frac{3}{5}$

• $\frac{4}{5}$

• $\frac{4}{3}$

• $\frac{5}{4}$

Tags

CCSS.HSG.SRT.C.6

A helicopter is hovering at an elevation of 500 feet off of the level ground. How many feet away is Jeff, who is on the ground looking up at the helicopter at a 30-degree angle of elevation?

• 
  

  $500$
  

• $500\sqrt{2}$

• $500\sqrt{3}$

• $1,000$

• $1,200$

Tags

CCSS.HSG.SRT.C.8

Toyba travels east 10 miles, then travels northwest at an angle of 25 degrees in a straight line until she is directly north of her original position. Assuming she has traveld on a completely flat surface, what is her straight-line distance from her original spot to the nearest tenth of a mile?

• 4.2

• 4.7

• 4.9

• 5.1

• 9.1

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

In a triangle similar to this one, in which the shortest side is 15, what will be the tangent of the larger non-right angle?

• 
  

  $\frac{12}{5}$
  

• $\frac{13}{12}$

• $1$

• $12$

• $13$

Tags

CCSS.HSG.SRT.C.6

What is the cosine of angle X?

• 
  

  $\frac{x}{y}$
  

• $\frac{y}{x}$

• $\frac{y}{\sqrt{x^2+y^2}}$

• $\frac{\sqrt{x^2+y^2}}{y}$

• $\frac{x}{\sqrt{x^2+y^2}}$

Tags

CCSS.HSG.SRT.C.6

Which of the following expressions would equal angle N ?

• 
  

  $\tan\left(\frac{n}{l}\right)$
  

• $\tan^{-1}\left(\frac{n}{l}\right)$

• $\sin\left(\frac{l}{m}\right)$

• $\sin^{-1}\left(\frac{l}{m}\right)$

• $\cos^{-1}\left(\frac{m}{n}\right)$

Tags

CCSS.HSG.SRT.C.8

The law of cosines states that

 $c^2=a^2+b^2-2ab\ \cos\ C$  in a triangle.  What would be the expression to solve for the line AB ?

•  $\sqrt{10^2+22^2-2\cdot10\cdot22\ \cos\ 30}$  

•  $\sqrt{10^2+22^2-2\cdot10\cdot22\ \cos\ 45}$  

•  $\sqrt{10^2+8^2-2\cdot10\cdot22\ \cos\ 45}$  

•  $\sqrt{10^2+8^2-2\cdot10\cdot22\ \cos\ 95}$  

•  $\sqrt{10^2+22^2-2\cdot10\cdot22\ \cos\ 105}$  

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

If $\theta$  is between 0 and  $\frac{\pi}{2}$  and has a tangent of $\frac{5}{12}$  , what is the cosine of $\theta$ ?

•  $\frac{5}{12}$  

•  $\frac{12}{5}$  

•  $\frac{5}{13}$  

•  $\frac{12}{13}$  

•  $\frac{13}{12}$  

Tags

CCSS.HSF.TF.C.8

By which of the following fractions would you multiply angle X that is expressed in degrees to convert it to radians?

• 
  

  $\frac{\pi}{45}$
  

• $\frac{\pi}{90}$

• $\frac{\pi}{180}$

• $\frac{\pi}{360}$

• $\frac{90}{\pi}$

Tags

CCSS.HSF.TF.A.1

The application of which of the following operators would enable one to solve for $\theta$ in the equation  $\sin\left(\theta\right)=\frac{2}{5}$  in only one further step?

•  $\cos^{-1}$  

•  $\sin^{-1}$  

•  $\tan^{-1}$  

•  $\sin$  

•  $\cos$  

Tags

CCSS.HSF.TF.B.7