Geometry and TrigonometryVery hardArea of a right triangle from a cosine and the hypotenuse
Geometry and Trigonometry practice question
In right triangle ABC, the right angle is at C, the hypotenuse AB has length 20, and cos A = 0.6. What is the area of the triangle?
Answer: 96
cos A = AC/AB, so AC = 20 × 0.6 = 12. Then BC = √(400 − 144) = 16, and the area is (1/2)(12)(16) = 96.
Common wrong answers
- If you answered 12
- 12 is the leg AC, not the area.
- If you answered 120
- 120 is (1/2)(12)(20), using the hypotenuse as a leg.
- If you answered 192
- 192 omits the 1/2 in the area formula.
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