2020 · Q67
If the angles of a triangle are 30° and 45° and the included side is (√3+1) cm, then what is the area of the triangle?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A(√3+1) cm²
- B(√3+3) cm²
- C(1/2)(√3+1) cm²
- D2(√3+1) cm²
Explanation
The third angle is 180° − 30° − 45° = 105°. With included side c = √3 + 1 between the 30° and 45° angles, area = c²·sin30°·sin45°/(2·sin105°) = 2(2+√3)(½)(√2/2)/(2·√2(√3+1)/4) = (√3 + 1)/2. Numerically the area is about 1.366 square units.