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Question

In a triangle ABC, if AB=7, BC=5 and CA=3, if the projection of BC on CA is equal to n2, then the value of n is


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Solution

Finding the projection of BC on CA and the value of n

Given the sides of a triangle are,

AB=a=7

BC=b=5

CA=c=3

The figure is as shown:

Projection of BC on CA=BCcosθ, which implies that,

CM=BCcosθ=BCb2+c2-a22bc=525+9-4930=534-4930=5-1530=52

Comparing this with n2, we get, n=5

Therefore, the value of n is equal to 5.


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