Geometry and TrigonometryVery hardSum of a sine and a cosine
Geometry and Trigonometry practice question
In right triangle ABC, angle C is the right angle, AC = 8 and BC = 6. What is the value of sin A + cos A?
Answer: 1.4 or 7/5
The hypotenuse is √(8² + 6²) = 10. sin A = BC/AB = 6/10 and cos A = AC/AB = 8/10. Their sum is 14/10 = 1.4.
Common wrong answers
- If you answered 1
- 1 is sin²A + cos²A, which is always 1 — but the question asks for the sum of sin A and cos A, not of their squares.
- If you answered 0.2
- 0.2 is cos A − sin A (0.8 − 0.6).
- If you answered 1.75
- 1.75 is 6/8 + 8/8, using the leg AC as the hypotenuse; the hypotenuse is 10.
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