In this worksheet, we will practice finding lengths in 30-60-90-degree triangles.

**Q1: **

Find the value of in the given figure.

**Q2: **

Find the length of in the figure to two decimal places.

**Q5: **

Find the length of .

**Q6: **

Consider triangle .

Find, in the form 1 : , the ratio of the side lengths : .

- A1 : 1
- B1 : 3
- C1 :
- D1 : 2
- E1 :

Find, in the form 1 : , the ratio of the side lengths : .

- A1 :
- B1 :
- C1 : 1
- D1 : 2
- E1 : 3

**Q7: **

In triangle , the length of is .

Find, in terms of , the length of .

- A
- B
- C
- D
- E

Find, in terms of , the length of .

- A
- B
- C
- D
- E

**Q8: **

Given that , and is a median in , find the perimeter of .

**Q9: **

Find the lengths of and .

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

**Q10: **

Given a right-angled triangle in which angle measures , which of the following is equal to the length of the side opposite to angle ?

- A half the length of the side opposite to the angle measuring
- B the length of the hypotenuse
- C one-third the length of the hypotenuse
- D half the length of the hypotenuse