Saturday 12 November 2011

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)

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