Allday Education

Free Special Right Triangles Worksheet

Ten special-right-triangle problems (45-45-90 and 30-60-90) with a worked answer key.

Answer key included
Name: Date:
Special Right Triangles
1.
In a 30°-60°-90° triangle, the shorter leg measures 33. Find the length of the longer leg.
33
??
60∘60^\circ
30∘30^\circ
2.
The legs of a 45°-45°-90° triangle each measure 1414. Find the length of the hypotenuse.
1414
1414
??
45∘45^\circ
45∘45^\circ
3.
The legs of a 45°-45°-90° triangle each measure 1717. Find the length of the hypotenuse.
1717
1717
??
45∘45^\circ
45∘45^\circ
4.
The legs of a 45°-45°-90° triangle each measure 66. Find the length of the hypotenuse.
66
66
??
45∘45^\circ
45∘45^\circ
5.
In a 30°-60°-90° triangle, the shorter leg measures 1313. Find the length of the hypotenuse.
1313
??
60∘60^\circ
30∘30^\circ
6.
The legs of a 45°-45°-90° triangle each measure 44. Find the length of the hypotenuse.
44
44
??
45∘45^\circ
45∘45^\circ
7.
The legs of a 45°-45°-90° triangle each measure 1212. Find the length of the hypotenuse.
1212
1212
??
45∘45^\circ
45∘45^\circ
8.
The legs of a 45°-45°-90° triangle each measure 77. Find the length of the hypotenuse.
77
77
??
45∘45^\circ
45∘45^\circ
9.
In a 30°-60°-90° triangle, the shorter leg measures 77. Find the length of the longer leg.
77
??
60∘60^\circ
30∘30^\circ
10.
In a 30°-60°-90° triangle, the shorter leg measures 22. Find the length of the longer leg.
22
??
60∘60^\circ
30∘30^\circ
Andy · alldayeverydaymath.com
Name: Answer KeyDate:
Special Right Triangles
1.
In a 30°-60°-90° triangle, the shorter leg measures 33. Find the length of the longer leg.
33
??
60∘60^\circ
30∘30^\circ
Answer: 333\sqrt{3}
2.
The legs of a 45°-45°-90° triangle each measure 1414. Find the length of the hypotenuse.
1414
1414
??
45∘45^\circ
45∘45^\circ
Answer: 14214\sqrt{2}
3.
The legs of a 45°-45°-90° triangle each measure 1717. Find the length of the hypotenuse.
1717
1717
??
45∘45^\circ
45∘45^\circ
Answer: 17217\sqrt{2}
4.
The legs of a 45°-45°-90° triangle each measure 66. Find the length of the hypotenuse.
66
66
??
45∘45^\circ
45∘45^\circ
Answer: 626\sqrt{2}
5.
In a 30°-60°-90° triangle, the shorter leg measures 1313. Find the length of the hypotenuse.
1313
??
60∘60^\circ
30∘30^\circ
Answer: 2626
6.
The legs of a 45°-45°-90° triangle each measure 44. Find the length of the hypotenuse.
44
44
??
45∘45^\circ
45∘45^\circ
Answer: 424\sqrt{2}
7.
The legs of a 45°-45°-90° triangle each measure 1212. Find the length of the hypotenuse.
1212
1212
??
45∘45^\circ
45∘45^\circ
Answer: 12212\sqrt{2}
8.
The legs of a 45°-45°-90° triangle each measure 77. Find the length of the hypotenuse.
77
77
??
45∘45^\circ
45∘45^\circ
Answer: 727\sqrt{2}
9.
In a 30°-60°-90° triangle, the shorter leg measures 77. Find the length of the longer leg.
77
??
60∘60^\circ
30∘30^\circ
Answer: 737\sqrt{3}
10.
In a 30°-60°-90° triangle, the shorter leg measures 22. Find the length of the longer leg.
22
??
60∘60^\circ
30∘30^\circ
Answer: 232\sqrt{3}
Andy · alldayeverydaymath.com

Scroll to see all 10 problems and the answer key on its own page. Printing includes every page.

About this worksheet

Students use the fixed side ratios of the 45-45-90 and 30-60-90 triangles to find a missing side. These two triangles show up constantly in trig and on the SAT, so the ratios are worth over-practicing.

Want this in multiple choice? Harder numbers? 30 versions?

Built for math teachers. Andy generates custom worksheets across Pre-Algebra, Algebra 1, Geometry, and Algebra 2 with exact answer keys.

Try it for $1

More free worksheets

Distance and Midpoint

Print free

Triangle Angle Sum

Print free