Geometry and TrigonometryEasy–MediumSine as a ratio of sides
Geometry and Trigonometry practice question
In right triangle ABC, the right angle is at C. The side opposite angle A has length 3, and the hypotenuse has length 5. What is the value of sin A?
- A. 3/5Correct
- B. 4/5
- C. 3/4
- D. 5/3
Answer: A. 3/5
The sine of an acute angle in a right triangle is opposite over hypotenuse. For angle A that's 3/5.
Why the other answers are wrong
- B. 4/5
- 4/5 is adjacent over hypotenuse, which is cos A. (The adjacent side is 4, by the Pythagorean theorem.) Sine uses the OPPOSITE side.
- C. 3/4
- 3/4 is opposite over adjacent, which is tan A. Sine divides by the hypotenuse.
- D. 5/3
- 5/3 is the ratio upside down. Sine is opposite/hypotenuse, and it can never exceed 1.
More Geometry and Trigonometry questions
- Easy–Medium
A circle has a radius of 6. What is its area? (Use A = πr².) - Easy–Medium
A right triangle has legs of length 6 and 8. What is the length of the hypotenuse? - Easy–Medium
A circle has a radius of 5. What is its circumference? (Use C = 2πr.) - Easy–Medium
What is the midpoint of the segment joining the points (2, 3) and (8, 11)? - Easy–Medium
What is the measure, in degrees, of angle B? - Easy–Medium
What is the area, in square centimeters, of the trapezoid?
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