In a right triangle XYZ, how do you determine the value of tan Y?

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To determine the value of tan Y, we need to recall the definition of the tangent function in the context of a right triangle. The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.

Consider triangle XYZ where:

  • X is one of the vertices of the right angle,
  • Y is the angle for which we want to find the tangent value, and
  • Z is the third vertex.

In this triangle:

  • The side opposite to angle Y is the length of segment XZ.
  • The side adjacent to angle Y is the length of segment XY.

Using this information, we can express the tangent of angle Y as:

tan Y = (length of XZ) / (length of XY)

To find the specific value of tan Y, you will need the actual measurements of sides XZ and XY. Plug those values into the equation, and you will have the tangent of angle Y.

For instance, if the length of XZ is 3 units and the length of XY is 4 units, then:

tan Y = 3 / 4 = 0.75

In summary, to calculate tan Y in triangle XYZ, take the length of the side opposite angle Y and divide it by the length of the side adjacent to angle Y.

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