# 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. Q3:

Find the length of . Q4:

Find the values of and . • A,
• B,
• C,
• D,
• E,

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.

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. Q17:

Triangles and are similar. What is the length of ? Q18:

Find the value of . • A
• B2
• C
• D