If ∆xyz ~ ∆bac find sin a, cos a and tan a explain!

Sin A =    2sqrt(5)/5

Cos A =    sqrt(5)/5

Tan A = 2

Step-by-step explanation:

If the triangles are similar, the sin, cos and tan values will be the same on either triangle.

So Sin A = Sin Y

Sin Y = opposite / hypotenuse

          = 6/3 sqrt(5)

We do not leave sqrt's in the denominator.  Multiply by sqrt(5)/sqrt(5)

           6 sqrt(5) / 3 sqrt(5)*sqrt(5)

          6sqrt(5) / 15

          2sqrt(5)/5

The third side of the triangle is found by the Pythagorean theorem

YZ^2 +6^2 = (3sqrt(5))^2

yz^2 +36 = 9*5

YZ^2 +36 = 45

YZ^2 +36-36 = 45-36

YZ^2 = 9

Take the square root

YZ =3

Cos Y = adjacent / hypotenuse

           = 3/3sqrt(5)

           = 1/sqrt(5)

We do not leave sqrt's in the denominator.  Multiply by sqrt(5)/sqrt(5)

            = sqrt(5)/sqrt(5)*sqrt(5)

                sqrt(5)/5

Tan Y = oppositie/adjancent

          =6/ 3

          =2

Since They are the same for Y or A

Sin A =    2sqrt(5)/5

Cos A =    sqrt(5)/5

Tan A = 2

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step-by-step explanation:

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step-by-step explanation:

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