# Trigonometry Special Right Triangles Worksheet

Trigonometry Special Right Triangles Worksheet
• Page 1
1.
What is the value of cos C in the right triangle ABC? [Given $x$ = 7 units, $y$ = 24 units and $a$ = 25 units.]

 a. $\frac{25}{7}$ b. $\frac{7}{25}$ c. $\frac{24}{25}$ d. $\frac{25}{24}$

2.
If the length of the leg opposite the 30° angle in a 30°- 60° - 90° triangle is 21 cm, then the length of the side opposite the 60° angle is
 a. 21$\sqrt{3}$ cm b. 24 cm c. 6$\sqrt{3}$ cm d. 6 cm

3.
If the length of the hypotenuse of a 30° - 60° - 90° triangle is 8$\sqrt{3}$ cm, then the length of the leg opposite the 60° angle is
 a. $\sqrt{3}$ cm b. 12 cm c. 8$\sqrt{3}$ cm d. 2$\sqrt{3}$ cm

4.
If the length of the hypotenuse of a 30° - 60° - 90° triangle is 22 cm, then the length of the leg opposite to 30° angle is
 a. 10$\sqrt{3}$ cm b. 1 cm c. 11 cm d. 20$\sqrt{2}$ cm

5.
In a 30o - 60o - 90o triangle, find the ratio of the legs.
 a. 1 : 2 b. 1 : $\sqrt{3}$ c. 2 : $\sqrt{3}$ d. 1 : 1

6.
The difference between the lengths of the legs in a 30o- 60o- 90o triangle is (8$\sqrt{3}$ + 8) cm. Find the length of the shorter leg.
 a. ($\sqrt{3}$ - 8) cm b. (16$\sqrt{3}$ + 8) cm c. (16 + 8$\sqrt{3}$) cm d. (16 - 8$\sqrt{3}$) cm

7.
What is the value of sin 45o?
 a. 0.866 b. 0.7071 c. 0.5

8.
Find the value of tan $A$, if sin $A$ = $\frac{3}{5}$ and cos $A$ = $\frac{4}{5}$.
 a. 1 b. $\frac{4}{3}$ c. $\frac{3}{4}$ d. $\frac{3}{5}$

9.
Find the value of tan Q in right triangle PQR for $x$ = 7 units, $y$ = 24 units and $a$ = 25 units.

 a. $\frac{7}{24}$ b. $\frac{7}{25}$ c. $\frac{25}{7}$ d. $\frac{24}{7}$

If tan 6° = $\frac{36}{x}$, then find the value of $x$.