Chapter 2 - Acute Angles and Right Triangles - Section 2.1 Trigonometric Functions of Acute Angles - 2.1 Exercises - Page 53: 79c

The length of the perpendicular leg is $\sqrt{3}~k$

We can use the Pythagorean theorem to find the length $L$ of the perpendicular leg: $L^2 = (2k)^2-k^2$ $L^2 = 3k^2$ $L = \sqrt{3k^2}$ $L = \sqrt{3}~k$ The length of the perpendicular leg is $\sqrt{3}~k$