(a) The sides of an isosceles triangle triangle are in the ratio (7 : 5 : 7). Calculate, correct to the nearest degree, the angle included between the equal sides.
(b) The sum of the interior angles of a regular polygon is 1440°. Calculate : (i) the number of sides ; (ii) the size of one exterior angle of the polygon.
Explanation
(a)
(5^{2} = 7^{2} + 7^{2} – 2(7)(7) cos theta)
(25 = 98 – 98 cos theta)
(cos theta = frac{98 – 25}{98})
(cos theta = 0.7449)
(theta = cos^{-1} (0.7449))
(approxeq 42°).
(b) (i) ((2n – 4) times 90° = 1440°)
(2n – 4 = frac{1440}{90} = 16)
(2n = 16 + 4 = 20)
(n = 10)
(ii) Size of exterior angle = (frac{360}{text{Number of sides}})
= (frac{360}{10})
= (36°)