A balloon 150 meters from the observer is rising vertically at constant rate. After 1 minute the angle of elevation is 28 degrees and 29 minutes. What is the angle after 3 minutes?

Question

Illustrate a mathematical scene of a bright red balloon, 150 meters away from an observer, ascending vertically at a constant speed. The observer is at ground level, watching the balloon with a professional-grade theodolite instrument used to measure angles. After 1 minute of launch, depict the balloon at an angle of elevation of 28 degrees and 29 minutes with respect to the viewer's line of sight. In the background, show the clear blue sky as a hint towards the balloon's further journey upwards after 3 minutes.

A balloon 150 meters from the observer is rising vertically at constant rate. After 1 minute the angle of elevation is 28 degrees and 29 minutes. What is the angle after 3 minutes?

Answer 1

tan(28deg59min)= h/150

h= 83.0893 m/min

@3 min
tan(theta)= h(@3min)/150
theta= arctan [(83.0893*3min)/150]
theta= 58.9621 deg

Answer 2

thanks big help

Answer 3

First get the height from its initial position

(Tan28°29') = h / 150
h= 83. 089
Now we will get the angle of the balloon from the observer after 3 mins. (3mins = 3 altitude)

(Tanθ) = (hx3) / 150
(Tanθ) = (83.089x3) / 150
θ = 58.96 deg

Answer 4

Well, let me put on my balloon hat and calculate that for you!

To find the angle after 3 minutes, we first need to find the rate at which the angle is changing.

In this case, the angle of elevation is changing linearly with time, since the balloon is rising at a constant rate.

So, if the angle after 1 minute is 28 degrees and 29 minutes, we can say that the rate of change is 29 minutes per 1 degree.

Now, to find the angle after 3 minutes, we simply multiply this rate by the number of minutes (3).

So, 29 minutes per 1 degree multiplied by 3 minutes gives us... *drum roll please*... 87 minutes per 3 degrees!

Therefore, after 3 minutes, the angle of elevation is approximately 28 degrees and 87 minutes.

Keep in mind that my calculations might not be 100% accurate, but hey, close enough for a clown, right?

Answer 5

To find the angle after 3 minutes, we need to use the given information and make some calculations. Let's break it down step by step:

1. Start with the given angle after 1 minute: 28 degrees and 29 minutes.

2. Convert the minutes to degrees: Since there are 60 minutes in one degree, we divide 29 minutes by 60 to get the decimal equivalent. 29 minutes / 60 minutes = 0.4833 degrees.

3. Add the converted minutes to the original angle of 28 degrees: 28 degrees + 0.4833 degrees = 28.4833 degrees.

4. The balloon is rising vertically, which means the angle of elevation remains constant over time. Therefore, the angle after 3 minutes will be the same as the angle after 1 minute.

5. So, the angle after 3 minutes is 28.4833 degrees.

Answer 6

You're so stupid!!!

Answer 7

To figure the height after 1 minute,

h/150 = tan 28°29'

Now, having h, you know that 3h is the altitude after 3 minutes. So, find the angle θ such that

tanθ = 3h/150

Or, in one step,

θ = arctan(3*150*tan28°29')