MATHEMATICS - OBJECTIVE -1

5. The sides of a triangle are in the ratio 1 :√3: 2,then the angles of the triangle are in the ratio 

(a) 1:3:5                               (b) 2:3:4 

(c) 3:2:1                               (d) 1:2:3

answer (d)

Answer:explanation

hypotenuse = √(a² + b²) 

                  = √(1² + √3²) = 2 (since 2 is the biggest,among 3)

Sin θ = base/hypotenuse = 1/2 =0.5

So, Angle θ = 30°

We know that second angle is 90° ( right angled traingle)

Hence, the third angle is 180 - (30+90) =60°

So answer is 30:60:90 = 1:2:3

 This indicates that a shadow and its source can be compared using ratios and the length of the structure can be estimated from the shadow of its full structure.

Ratio analysis is often used in trigonometry and algebric equations as Simultaneous equations are solved in a digital Scientific calculator using Ratio analysis method .For this ,if it is a third degree equation, solution can be obtained by three equations containing three variables. This method has been mentioned in ' Abacus ',solution techniques ,where easy solutions are found using counting beads in an abacus board .