I'm fine with angle of elevation problem, but angle of depression problems are tricky for me. Is this right?
From a balloon 835 m high, a command post is seen with an angle of depression of 7 degrees. How far is it from the point on the ground directly below the balloon to the command post?
I drew a picture and thought that I would say
Tan of 83= x/835
Then i got 6800.53
Is that right?
yes
To solve angle of depression problems, it's important to make sure you have a clear understanding of the situation. In this case, you have a balloon 835 m high and you're trying to find the distance from the point on the ground directly below the balloon to the command post using the given angle of depression.
Your approach with the tangent function is correct. Let's break it down step by step:
1. Draw a diagram: Start by drawing a diagram to visualize the problem. Draw a vertical line to represent the balloon, label it as 835 m. Then draw a horizontal line from the base of the balloon to represent the ground. Label this distance as 'x' since it's what we're trying to find. Finally, draw a line from the top of the balloon to the command post, making an angle of depression of 7 degrees.
2. Identify the trigonometric function: In angle of depression problems, you typically use the tangent function. This is because the tangent of an angle is defined as the ratio of the opposite side to the adjacent side.
3. Set up the equation: From the diagram, you can see that the opposite side is the height of the balloon (835 m) and the adjacent side is the distance from the point on the ground directly below the balloon to the command post (x). Therefore, the equation becomes:
tan(7°) = 835 / x
4. Solve for 'x': Rearrange the equation to isolate 'x':
x = 835 / tan(7°)
5. Calculate the value: Evaluating the above equation, you get:
x ≈ 6800.53 m
So, your calculation of 6800.53 m is correct!
The distance from the point on the ground directly below the balloon to the command post is approximately 6800.53 meters.