Answer:
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
