In a right-angled triangle, the leg lying opposite an angle of 60 degrees is 3√3 cm.

In a right-angled triangle, the leg lying opposite an angle of 60 degrees is 3√3 cm. Find the other sides of this triangle and the area.

1. A, B, C – the vertices of the triangle. ∠С = 90 °. ВС = 3√3 cm. ∠А = 60 °. S is the area of the triangle.

2. We calculate the length AB through the sine ∠A.

Sine ∠A is the quotient of dividing the length of the BC leg, located opposite this angle (opposite), by the length of the hypotenuse AB.

Sine 60 ° = √3 / 2.

BC / AB = √3 / 2.

AB = BC: √3 / 2 = 3√3: √3 / 2 = 6 cm.

3. AC = √AB² – BC² (by the Pythagorean theorem).

AC = √6² – (3√3) ² = √36 – 27 = √9 = 3 cm.

4. S = АС х ВС / 2 = 3 х 3√3 / 2 = 4.5√3 cm².

Answer: S = 4.5√3 cm², AB = 6 cm, AC = 3 cm.



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