In a triangle ABC, the lengths of the sides AB and AC equal 17.5cm and 9cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD=3cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?
(1)17.05 (2) 27.85 (3) 22.45 (4) 32.25 (5) 26.25
Solution follows here:
It is a simple formula based trigonometric one.
Given: AB = c = 17.5;AC = b = 9; Let base = BC = a; height = AD = 3;
To find: circum radius = R
Area of the triangle ABC = Δ = ½ (BC)(AD) = ½ (a)(3) = 3a/2
The formula here is : R = abc/4Δ = abc / 4(3a/2) = bc/6 = (17.5)(9)/6 = 26.25Answer (5)