Geometry and TrigonometryMediumSpecial right triangles (45-45-90)
Geometry and Trigonometry practice question
In a 45°-45°-90° right triangle, each leg has length 5. What is the length of the hypotenuse?
- A. 5
- B. 5√2Correct
- C. 10
- D. 5√3
Answer: B. 5√2
In a 45-45-90 triangle the hypotenuse is a leg times √2, so 5√2. (Choice D, 5√3, is the pattern for a 30-60-90 triangle.)
Why the other answers are wrong
- A. 5
- 5 is just the leg length again; the hypotenuse of a right triangle is always longer than either leg, here 5√2.
- C. 10
- 10 is 5 + 5 (or 2 × 5), but the 45-45-90 hypotenuse is a leg times √2, not times 2.
- D. 5√3
- 5√3 is the 30-60-90 pattern. For 45-45-90, the hypotenuse is leg × √2 = 5√2.
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