Geometry and TrigonometryVery hardSum of the sine and cosine of an angle
Geometry and Trigonometry practice question
A right triangle has legs of length 7 and 24. Let θ be the acute angle opposite the leg of length 7. What is the value of sin θ + cos θ?
Answer: 31/25 or 1.24
The hypotenuse is 25. sin θ = 7/25 and cos θ = 24/25, so the sum is 31/25.
Common wrong answers
- If you answered 1
- 1 confuses sin θ + cos θ with sin²θ + cos²θ, which equals 1.
- If you answered 7/25
- 7/25 is sin θ alone.
- If you answered 31/24
- 31/24 adds the legs but divides by the wrong side; both ratios are over the hypotenuse, 25.
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