at a certain time of the day a tree casts a shadow of 5ft. find the ht. of the tree if tan.A = 5/6.

Please follow directions:

School Subject: _________ (Examples: math, science, algebra, geography)

If A is the angle of elevation of the sun, then

tanA = height/shadowlength

So,

height/5 = 5/6

Looks like you need to review the basic trig functions. And always draw a diagram!

To find the height of the tree, we can use the tangent function. The tangent of an angle is defined as the ratio between the opposite side and the adjacent side of a right triangle.

In this case, let's assume that A is the angle of elevation from the ground to the top of the tree, and the adjacent side is the length of the shadow (5ft). We want to find the opposite side, which represents the height of the tree.

Using trigonometry, we can write:

tan(A) = opposite/adjacent

Given that tan(A) = 5/6, we can substitute this value into the equation:

5/6 = opposite/5

To solve for the opposite side (height of the tree), we can cross-multiply:

6 * opposite = 5 * 5
6 * opposite = 25

Divide both sides by 6:

opposite = 25/6

Therefore, the height of the tree is approximately 4.17 feet (25/6 = 4.17).