Theory question 104
Trigonometry(a) The sides of an isosceles 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.
Show the model answer
Model answer
(a) Take sides 7, 7 and 5. The line from the apex to the middle of the base splits it into right-angled triangles: sin(½θ) = 2.5/7 = 0.3571, ½θ ≈ 20.9°, θ ≈ 42°.
(b)(i) (n − 2) × 180 = 1440, so n − 2 = 8 and n = 10.
(ii) Exterior angle = 360 ÷ 10 = 36°.
Explanation
The equal sides meet at the apex; the side in the ratio that differs is the base.