Math, asked by Sarikasree, 5 months ago

In ∆ABC and ∆XYZ , if angleX are acute angles such that Cos A = cos X then Show that angle A = angle X.





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Answers

Answered by neha42476
3

Answer:

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!

Step-by-step explanation:

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Answered by jaat1371
1

Step-by-step explanation:

cos A = b/h

cos X = b/h

given--- cosA = cosX--------(1)

on compairing eq. no. (1) we get

angle A = angle B

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