The angle of elevation of a tree at a place 80m away is 12 degree 5 minute.what is a height of tree?

To find the height of the tree, we can use trigonometry and the given angle of elevation.

First, let's convert the angle of elevation from degrees and minutes to decimal degrees.
12 degrees + 5 minutes = 12 + (5/60) degrees = 12.0833 degrees (rounded to 4 decimal places).

Now, we can set up a right-angled triangle with the base being the distance from the tree to the observer (80m) and the height being the height of the tree (which we need to find). The angle of elevation (12.0833 degrees) will be the angle opposite the height of the tree.

Using trigonometry, we can use the tangent function to calculate the height of the tree. The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.

So, tan(angle) = height of the tree / distance to the tree.

Substituting the values we know:
tan(12.0833 degrees) = height of the tree / 80m.

To find the height of the tree, we rearrange the formula:
height of the tree = 80m * tan(12.0833 degrees).

Using a calculator, we can find the approximate value of the height of the tree:
height of the tree ≈ 80m * tan(12.0833 degrees) ≈ 16.257m (rounded to 3 decimal places).

Therefore, the height of the tree is approximately 16.257 meters.

h/80 = tan 12°5'