A base angle of an isosceles triangle measures 45 degrees and the length of one of the legs is 12. What is the length of the altitude drawn to the base of the triangle?

The length of the altitude drawn to the base of the triangle is 8.49

Step-by-step explanation:

In this question, we are asked to calculate the length of the altitude to the base of an isosceles triangle given the length of one of the legs and the base angle. To answer this sufficiently, we consider the diagram of the triangle in the attached file.

From the triangle , we can see that we want to calculate the length h.

Let’s look at a cut-out triangle from the big triangle. This is the triangle AOC

WE can calculate the length of h here, using trigonometric identity. What we have is the hypotenuse and the opposite, this means that the trigonometric identity to use is the sine

Sine 45 = h/12

h = 12 * sine 45

Sine 45 = 0.7071

h = 12 * 0.7071

h = 8.49