Right triangle trigonometric ratios Knowledge-Based Practice

Questions

1. 1.

   In a right triangle $ABC$ with the right angle at vertex $C$, the hypotenuse has length $AB = 25$ and $\tan A = \frac{3}{4}$. What is the area of triangle $ABC$?

   • A) 60
   • B) 120
   • C) 300
   • D) 150
2. 2.

   In a right triangle $ABC$ with the right angle at vertex $C$, $\cos A = \frac{4}{5}$. What is the value of $\frac{\tan A + \sec A}{\csc B}$?

   • A) $\frac{6}{5}$
   • B) $\frac{7}{5}$
   • C) $\frac{8}{5}$
   • D) $\frac{5}{2}$
3. 3.

   In a right triangle $DEF$ with right angle at vertex $E$, $\tan D = \frac{5}{12}$. What is the value of $\sec F - \cot D$?

   • A) $\frac{1}{5}$
   • B) $\frac{5}{13}$
   • C) $\frac{1}{12}$
   • D) $\frac{7}{12}$
4. 4.

   In a right triangle $KLM$ with the right angle at vertex $L$, $\cos K = \frac{3}{5}$ and the perimeter of the triangle is 48 cm. What is the length of side $LM$?

   • A) 16 cm
   • B) 12 cm
   • C) 20 cm
   • D) 15 cm
5. 5.

   In a right-angled triangle $ABC$ with the right angle at vertex $C$, the leg lengths are $AC = 15$ and $BC = 8$. What is the value of the product $\sin A \cos A$?

   • A) $\frac{64}{289}$
   • B) $\frac{120}{289}$
   • C) $\frac{225}{289}$
   • D) $\frac{8}{15}$

Answers and step-by-step solutions appear after you finish the test.