Trigonometry-2 (CAT-2008)

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:

Solution:

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 = 26.25

Answer (5)