GRE General TestQuantitative ReasoningEasy
A land surveyor is measuring a triangular plot of land. The lengths of two sides are 10 meters and 15 meters, and the angle between them is 30 degrees. What is the area of the triangular plot (in square meters)? (Use \(\sin(30^{\circ}) = 0.5\))
- A150.0
- B37.5
- C75.0
- D50.0
Show answer & explanationAnswer & explanation
Correct answer: B. 37.5
To find the area of a triangle given two sides and the included angle, use the formula: Area = (1/2)ab\(\sin(C)\), where a and b are the lengths of the sides and C is the included angle.
Why the other options are wrong
- A. This results from multiplying the two sides without the sine or 1/2 factor.
- C. This results from forgetting to multiply by 1/2 or using \(\sin(C)=1\).
- D. This results from a miscalculation, perhaps using 2/3 instead of 1/2 or other errors.
Area of a Triangle (SAS)
The area of a triangle can be calculated if the lengths of two sides and the measure of the included angle (Side-Angle-Side) are known.
- Formula: Area = (1/2)ab\(\sin(C)\)
- a and b are the lengths of the two sides.
- C is the measure of the angle included between sides a and b.
Memory trick: Half-AB-Sine-C: Remember the formula for side-angle-side area.