Geometry and TrigonometryHardAngle in a right triangle from its sides
Geometry and Trigonometry practice question
A right triangle has a hypotenuse of length 2√2 and one leg of length 2. What is the measure, in degrees, of the angle opposite that leg?
Answer: 45
The other leg is √((2√2)² − 2²) = √(8 − 4) = 2, so the legs are equal and the triangle is isosceles: each acute angle is 45°. (Equivalently, sin θ = 2/(2√2) = √2/2, so θ = 45°.)
Common wrong answers
- If you answered 30
- 30° would need the leg to be half the hypotenuse (√2), not 2.
- If you answered 60
- 60° would need the leg to be √3 times the shorter leg; here the legs are equal.
- If you answered 90
- The angle opposite a LEG can't be the right angle; that is opposite the hypotenuse.
More Geometry and Trigonometry questions
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