A 45-45-90 triangle has sides s, s, s2. A 30-60-90 triangle has sides s, s3, 2s, with the shortest side opposite 30°. Equilateral triangles split into two 30-60-90 triangles, and squares into two 45-45-90 triangles.
The trap
Putting 3 on the side opposite 30°.
Can Desmos do it?
These answers have radicals; Desmos gives decimals. Knowing the side patterns gets you the exact form.
College Board skill: Right triangles and trigonometry · Geometry and Trigonometry
Try one at each level
One question from each level. The drill has 12 at every level, and moves you up after four right in a row.
Level 1 · Warm-up
A square has a diagonal of length 122. What is the area of the square?
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Answer: 144A diagonal splits the square into two 45-45-90 triangles, so the side is 12 and the area is 122=144.
Level 2 · Test level
A right triangle has a 30° angle and a hypotenuse of length 14. What is the perimeter of the triangle?
A14+143
B21+73
C7+213
D21+72
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Answer: BThe side opposite 30° is half the hypotenuse, 7, and the other leg is 73. The perimeter is 14+7+73=21+73.
Level 3 · Beyond the test
In triangle ABC, angle B measures 30° and angle C measures 45°. The altitude from A to BC has length 16. What is the length of BC?
A32+162
B16+163
C16+162
D163
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Answer: BThe altitude AD splits BC into two pieces. Triangle ADC is 45-45-90, so DC=16. Triangle ADB is 30-60-90 with the altitude opposite the 30° angle, so BD=163. Then BC=16+163.
Practice all 36 questions
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