from your apartment balcony, you look down and see two of your friends walking toward your apartment building. As you look East, you see Maria with a 60 degree angle of depression. As you look East, you also see jack with a 45 degree angle of depression. If your apartment balcony is 15 feet above the ground, then how far apart are maria and jack?

Question

from your apartment balcony, you look down and see two of your friends walking toward your apartment building. As you look East, you see Maria with a 60 degree angle of depression. As you look East, you also see jack with a 45 degree angle of depression. If your apartment balcony is 15 feet above the ground, then how far apart are maria and jack?

Answer 1

Jack's distance from the building ---- x

tan45 = 15/x ----> x = 15
for Maria:
tan 60 = 15/y
y = 15/tan60 = appr 8.66 ft

they are 15-8.66 or 6.34 ft apart

Answer 2

To solve this problem, we can use trigonometry and the concept of angle of depression.

First, let's create a diagram to visualize the situation:

(Your Apartment Balcony - 15 ft above the ground)
--------------------------------------------- (East)
|\
| \
| \
| \ (Maria)
| \
| \
| \
| \
| \
| \
| \
| \
| \
| \
|______________\
(Jack)

In this diagram, we have your apartment balcony, Maria, and Jack.

Let's denote the distance from your apartment balcony to Maria as 'x', and the distance from your apartment balcony to Jack as 'y'.

We have two right-angled triangles formed by your apartment balcony and each friend, with the angle of depression as given in the problem.

For Maria's triangle:
Angle of depression = 60 degrees
Height = 15 ft
Distance = x

For Jack's triangle:
Angle of depression = 45 degrees
Height = 15 ft
Distance = y

Now, trigonometry tells us that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side:

For Maria's triangle:
Tangent(60°) = Opposite side / Adjacent side
Tangent(60°) = 15 ft / x

For Jack's triangle:
Tangent(45°) = Opposite side / Adjacent side
Tangent(45°) = 15 ft / y

To find the values of x and y, we can rearrange the equations:

x = 15 ft / Tangent(60°)
y = 15 ft / Tangent(45°)

Now, let's calculate the values of x and y:

x = 15 ft / Tan(60°)
≈ 15 ft / 1.732 (using a calculator)
≈ 8.66 ft

y = 15 ft / Tan(45°)
≈ 15 ft / 1 (using a calculator)
≈ 15 ft

Therefore, Maria and Jack are approximately 8.66 ft apart.

Answer 3

m and j

tan 30 = m/15
tan 45 = 1 = j/15
j - 15 and m = 15 tan 30 = 8.66
m+j = 23.7