In a right-angled triangle, the leg lying opposite an angle of 60 degrees is 3√3cm. Find the other two sides of this triangle and its area.
1. Vertices of the triangle – A, B, C. AB = 3√3 centimeters. ∠А = 90 °. ∠С = 60 °. S is the area of the triangle.
2. We calculate the length of the leg AC through one of the trigonometric functions ∠C (tangent):
AB / AC = tangent ∠C = tangent 60 ° = √3.
AC = AB: √3 = 3√3: √3 = 3 centimeters.
3. ВС = √АВ² + АС² (by the Pythagorean theorem).
BC = √ (3√3) ² + 3² = √27 + 9 = √36 = 6 centimeters.
4. S = AB x AC: 2 = 3√3 x 3: 2 = 4.5√3 centimeters².
Answer: S = 4.5√3 centimeters². AC = 3 centimeters. BC = 6 centimeters.
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