Right triangle trigonometric ratios Knowledge-Based Download PDF

Questions

1. 1.

   In a right triangle $ABC$ with right angle at $C$, the acute angle $A$ satisfies $\sin(A) = 2\cos(A)$. What is the value of $\sin(A)\cos(A)$?

   • A) $\frac{1}{5}$
   • B) $\frac{1}{2}$
   • C) $\frac{2}{5}$
   • D) $\frac{4}{5}$
2. 2.

   In a right triangle $DEF$ with right angle at $E$, the length of leg $DE$ is 14 and $\cos(D) = \frac{7}{25}$. What is the length of leg $EF$?

   • A) 24
   • B) 48
   • C) 50
   • D) 25
3. 3.

   In a right triangle with acute angle $\alpha$, the hypotenuse has length 25 and the side adjacent to $\alpha$ has length 20. What is the value of $\sin(\alpha) + \tan(\alpha)$?

   • A) $\frac{27}{20}$
   • B) $\frac{31}{20}$
   • C) $\frac{29}{15}$
   • D) $\frac{9}{20}$
4. 4.

   In a right triangle with acute angle $\theta$, if $\tan(\theta) = \frac{7}{24}$, what is the value of $\cos(\theta) - \sin(\theta)$?

   • A) $\frac{31}{25}$
   • B) $\frac{17}{25}$
   • C) $\frac{7}{25}$
   • D) $\frac{17}{24}$
5. 5.

   In a right triangle $ABC$ with right angle at $C$, if $\sin(A) = \frac{5}{13}$, what is the value of $\tan(B)$?

   • A) $\frac{5}{12}$
   • B) $\frac{12}{13}$
   • C) $\frac{12}{5}$
   • D) $\frac{13}{5}$