Question

3. Ted is standing on his balcony and sees his dog on the ground. The angle of depression to the dog is 40. Ted's eye level is 16 feet above the groundAt that moment, Ted drops a piece of his donut through the cracks of the balcony floor. How far must his dog walk to get to the donut?

Answer 1

Explanation:

Ted's balcony

|\

| \

| \ <- 40 degrees

| \

| \ <-- line of sight to the dog

| \

| \

| \

| \

| \

|__________\

Ted's

eye level

Let d be the distance the dog needs to walk to get to the donut. We can use trigonometry to solve for d.

Since the angle of depression from Ted's line of sight to the dog is 40 degrees, the angle between the ground and Ted's line of sight is 90 - 40 = 50 degrees.

We can use the tangent function to find d:

tan(50) = opposite / adjacent

The opposite side is the height of Ted's eye level above the ground, which is 16 feet. The adjacent side is d, the distance the dog needs to walk to get to the donut.

tan(50) = 16 / d

d = 16 / tan(50)

d ≈ 12.6 feet