Geometry and TrigonometryEasy–MediumSide from a sine and the hypotenuse
Geometry and Trigonometry practice question
In right triangle ABC, angle C is the right angle, sin A = 3/5, and the hypotenuse AB has length 15. What is the length of side BC?
Answer: 9
sin A = opposite/hypotenuse, and the side opposite angle A is BC. So BC/15 = 3/5, giving BC = 9.
Common wrong answers
- If you answered 3
- 3 is the numerator of the ratio, not the side; scale it by the hypotenuse: 15 × 3/5.
- If you answered 12
- 12 is the ADJACENT side, AC (using cos A = 4/5). BC is opposite angle A.
- If you answered 25
- 25 is 15 × 5/3, inverting the ratio.
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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