# Worksheet: Trigonometric Ratios in Right Triangles

In this worksheet, we will practice finding and express the values of the three trigonometric ratios—sine, cosine, and tangent—for a given angle in a right triangle.

**Q5: **

Find in the given figure. Give your answer to two decimal places.

**Q6: **

Find given is a triangle where and .

**Q7: **

Find given is a right-angled triangle at where .

**Q8: **

Find given is a rectangle where and .

- A
- B
- C
- D

**Q9: **

Find the value of .

- A
- B
- C
- D

**Q10: **

Find the value of given where is the smallest positive angle.

- A
- B
- C
- D

**Q11: **

Find the value of .

**Q12: **

Simplify .

**Q13: **

Simplify .

**Q14: **

Find the value of .

**Q15: **

Find given that is a right triangle at , where and .

- A
- B
- C
- D
- E

**Q16: **

Find the main trigonometric ratios of given is a right-angled triangle at where the ratio between and is .

- A , ,
- B , ,
- C , ,
- D , ,

**Q17: **

Find given that is a right-angled triangle at where and .

- A
- B
- C
- D

**Q18: **

Find the values of and giving the answer to three decimal places.

- A ,
- B ,
- C ,
- D ,

**Q19: **

In the triangle shown, is the side labelled adjacent to angle , opposite angle , or the hypotenuse?

- Ahypotenuse
- Badjacent
- Copposite

**Q21: **

Find the values of and giving the answer to three decimal places.

- A ,
- B ,
- C ,
- D ,

**Q22: **

is a right-angled triangle at , where , , and . Find the measure of giving the answer to the nearest second.

- A
- B
- C
- D

**Q23: **

Find the value of , given that is a triangle, where , , and is drawn perpendicular to intersecting at .

- A
- B
- C
- D

**Q24: **

Find the value of given is a right-angled triangle at where .

- A175
- B625
- C168
- D600

**Q25: **

is a point inside a square with a side length of 48 cm, where and . Find the value of , given that .

- A6
- B42
- C
- D