Question

Triangle XYZ has sides XY = 3", YZ = 4", and XZ = 5". If angle Y is a right angle, and side YZ is opposite angle X, what is the tan of angle X?

Express your answer as a decimal to three significant digits.

Answer 1

1.33

Explanation:

In triangle XYZ, we have:

XY = 3"

YZ = 4"

XZ = 5"

Given that angle Y is a right angle, this is a right triangle.

We're interested in finding the tangent of angle X. The tangent of an angle in a right triangle is given by the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

In this case, angle X is opposite side YZ and adjacent to side XY.

So, tan(X) = Opposite / Adjacent = YZ / XY = 4 / 3.

Now, let's calculate this value:

tan(X) = 4 / 3 = 1.333.

Therefore, the tangent of angle X is approximately 1.333 (rounded to three significant digits).