ACT Practice - Trigonometry

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

• 
  

  $\frac{3}{4}$
  

• $\frac{3}{5}$

• $\frac{4}{5}$

• $\frac{4}{3}$

• $\frac{5}{4}$

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?

• 
  

  $500$
  

• $500\sqrt{2}$

• $500\sqrt{3}$

• $1,000$

• $1,200$

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

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?

• 
  

  $\frac{12}{5}$
  

• $\frac{13}{12}$

• $1$

• $12$

• $13$

What is the cosine of angle X?

• 
  

  $\frac{x}{y}$
  

• $\frac{y}{x}$

• $\frac{y}{\sqrt{x^2+y^2}}$

• $\frac{\sqrt{x^2+y^2}}{y}$

• $\frac{x}{\sqrt{x^2+y^2}}$

Which of the following expressions would equal angle N ?

• 
  

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

• $\tan^{-1}\left(\frac{n}{l}\right)$

• $\sin\left(\frac{l}{m}\right)$

• $\sin^{-1}\left(\frac{l}{m}\right)$

• $\cos^{-1}\left(\frac{m}{n}\right)$

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 ?

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

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

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

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

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

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

•  $\frac{5}{12}$  

•  $\frac{12}{5}$  

•  $\frac{5}{13}$  

•  $\frac{12}{13}$  

•  $\frac{13}{12}$  

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

• 
  

  $\frac{\pi}{45}$
  

• $\frac{\pi}{90}$

• $\frac{\pi}{180}$

• $\frac{\pi}{360}$

• $\frac{90}{\pi}$

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?

•  $\cos^{-1}$  

•  $\sin^{-1}$  

•  $\tan^{-1}$  

•  $\sin$  

•  $\cos$