Triangle area: sine, Heron and the circles
Find the area of a triangle from two sides and the angle between them, or from three sides with Heron’s formula, then use the area to find the radii of the circle inside and the circle round a triangle.
- سوريا: الصف ١١
- إيران: الصف ١١
- أفغانستان: الصف ١٠
- أوكرانيا: الصف ٩
- روسيا: الصف ٩
- ألمانيا: الصف ١٠
- بريطانيا: السنة ١١
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
For Afghan Grade 10 (chapter 5: area from two sides and an angle, Heron’s formula, radii of the circumscribed and inscribed circles), Iran Grade 11 and GCSE. The triangles are drawn to scale (1 unit is 1 cm); some quantities are hidden.
The area of a triangle with sides a and b and the angle C between them is K = absinC٢.
With the semi-perimeter s = a + b + c٢, Heron’s formula gives the area from the three sides: K = √(s(s − a)(s − b)(s − c)).
The radius of the inscribed circle (inradius) is r = Ks. The radius of the circumscribed circle (circumradius) is R = abc٤K, which is also R = a٢sin A.