In triangleABC and triangle XYZ, if angleA and angleX are acute angles such that cosA=cosX then show that angleA=angleX.
Answer (1)
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!
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