Question

The top of a tree makes angles s and t with Points K and L on the ground, respectively, such that the angles are complementary. Point K is a x meters and Point L is y meters from the base of the tree. a. In terms of x and y, find the height of the tree. Include your work. Hint: what is triangle LGM?

Answer 1

To find the height of the tree, use trigonometry and the information about the angles and distances. Use the equation sin(s) = cos(t) and solve for the height of the tree in terms of x and y. The height of the tree can be calculated as (x * sin(s)) / cos(t).

Step-by-step explanation:

To find the height of the tree, we can use the concept of trigonometry and the given information about the angles and distances. Since the angles s and t are complementary, we know that sin(s) = cos(t). Let's consider triangle LGM, where L is the base of the tree, G is the top of the tree, and M is a point on the ground that is directly below G. In triangle LGM, sin(s) = height of the tree / x and cos(t) = height of the tree / y. Therefore, we can set up the equation sin(s) = cos(t) and solve for the height of the tree in terms of x and y.

sin(s) = height of the tree / x --> height of the tree = x * sin(s)

cos(t) = height of the tree / y --> height of the tree = y * cos(t)

Equating the two expressions for the height of the tree, we have x * sin(s) = y * cos(t). Rearranging the equation, we get:

Height of the tree = (x * sin(s)) / cos(t)