Given the right triangle XYZ, what is the value of tan(Y)?

Solution:

The above triangle is a right angled triangle in which ∠Z =90°

We know that

Tan(Y) = perpendicular/ base

Tan(Y) = XZ/YZ

Now ZY can be found out from expression below

sin(60°) = YZ/4

YZ = 4sin(60°)

sin(60°) = √3/2

YZ = 4 × √3/2

YZ = 2√3

Therefore

Similarly XZ can be found out as follows:

cos(60°) = XZ/XY

cos(60°) = XZ/4

cos(60°) = 1/2

XZ = 4 × 1/2 = 2

Tan Y = XZ/YZ = 2/2√3 = 1/√3

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Given the right triangle XYZ, what is the value of tan(Y)?

Summary:

Given the right triangle XYZ, what is the value of tan(Y) = 1/√3