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In triangleABC and triangle XYZ, if angleA and angleX are acute angles such that cosA=cosX then show that angleA=angleX.


Thanga Srivalli 11th Apr, 2020
Answer (1)
Awanya Dabas 11th Apr, 2020

Hey!

This is the solution:

We know that,

cosA= AB/ AC

cosX= XY/ XZ

Now, it is given that cosA= cosX

Therefore, AB/AC= XY/XZ

Let, these fractions be equal to k.

Therefore, AB= k.XY and AC= k.XZ ........(1)

Now, we need to find BC/ZY

So, BC/ZY= sqrt[AC^2- AB^2]/ sqrt[XZ^2- XY^2]

Putting the values from equation (1),

BC/ZY= k

Therefore, AB/XY= AC/XZ= BC/ZY

Therefore, the two triangles are similar.

And by property of similarity, angleA= angleX.

Hope this answer helps!

1 Comment
Comments (1)
7th Oct, 2020
How we got the formula that BC/YZ =
Reply

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