A 30ffoot tree cast a12 foot shadow find the measure of the angle of elevation of the sun to the nearest degree.

tanθ = 30/12

To find the angle of elevation of the sun, we can use the concept of similar triangles.

In this case, we have a right triangle formed by the tree, its shadow, and the rays of the sun. Let's denote the height of the tree as 'h' and the length of the shadow as 's'. We can establish the following proportion:

h / s = 30 / 12

To find the measure of the angle of elevation, we need to find the angle opposite to the height of the tree in the right triangle. We can use the inverse tangent function (tan^(-1)) to calculate this angle.

Let me calculate the answer for you:

First, let's solve the proportion to find the height:
h / 12 = 30 / 12
h = 30

Now, let's calculate the angle of elevation:
tan^(-1)(h / s) = tan^(-1)(30 / 12)

Using a calculator or trigonometric table, tan^(-1)(30 / 12) is approximately 68.19 degrees.

Therefore, the measure of the angle of elevation of the sun to the nearest degree is 68 degrees.