# Worksheet: Special Right Triangles

In this worksheet, we will practice finding lengths in 30-60-90-degree and in 45-45-90-degree triangles without trigonometry.

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

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

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

**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 ?

- Athe length of the hypotenuse
- Bone-third the length of the hypotenuse
- Chalf the length of the side opposite to the angle measuring
- Dhalf the length of the hypotenuse

**Q11: **

Find the length of .

**Q12: **

In the figure below, , is the midpoint of , and . Given that , find the length of .

- A14 cm
- B12 cm
- C13 cm
- D11.26 cm
- E16.25 cm

**Q13: **

Given that is a rectangle, find the length of .

**Q14: **

If the perimeter of a rhombus is 88 cm, and the measure of one of its angles is , find its area approximated to the nearest integer.

- A484 cm
^{2} - B838 cm
^{2} - C242
cm
^{2} - D419 cm
^{2}

**Q15: **

In the trapezoid , . Find the area of in square feet. Round your answer to the nearest tenth.

**Q16: **

Use the information in the figure to determine the area of the square.