1) two hot-air balloons are 48.2 m and 61.0 m above the ground. A person in the left balloon observes that the right balloon is 13.3° above the horizontal. What is the horizontal distance x between the two balloons?
The left balloon is 48.2m and the right balloon is 61.0m.
I am not sure how to start this problem.
tan13.3º =(61-48.2)/x
x =12.8/tan13.3º =54.1 m
How do you know when to use tan instead of cos or sin?
Horizontal leg (the first cathetus) is the distance between vertical lines connecting each of the baloons with the ground; the vertical leg (the second cathetus) is difference between heights; the hypothenuse is separation between two baloons.
Accotding to difinition
tan α = opposite side/adjacent side.
In the problem you know the opposite side (the second cathetus) and the angle, and you must find the first cathetus.
Horizontal leg (the first cathetus) is the distance between vertical lines connecting each of the baloons with the ground; the vertical leg (the second cathetus) is difference between heights; the hypothenuse is separation between two baloons.
Accotding to difinition
tan α = opposite side/adjacent side.
In the problem you know the opposite side (the second cathetus) and the angle, and you must find the first cathetus.
Well, it seems like those hot-air balloons are playing a game of "I can see you, but you can't see me!" Let's help them out.
To solve this problem, we'll need to use some trigonometry. We have the height of the left balloon (48.2 m) and the angle (13.3°) that the right balloon makes with the horizontal. What we want to find is the horizontal distance (x) between the two balloons.
Now, let's imagine a right triangle formed by the horizontal distance (x), the height of the left balloon (48.2 m), and the height of the right balloon (61.0 m). The angle between the left balloon's height and the horizontal distance is 90° - 13.3°.
Using the tangent function, we can set up the equation:
tan(90° - 13.3°) = (61.0 m - 48.2 m) / x
Simplifying this equation, we have:
tan(76.7°) = 12.8 m / x
Now, to find x, we can solve for it:
x = 12.8 m / tan(76.7°)
Plug this into your calculator, and you'll get the value of x. So, my dear friend, you're just a few button presses away from finding the horizontal distance between those two balloons. Good luck!
To solve this problem, we can use trigonometry and create a right triangle. Let's assume the horizontal distance between the two balloons is represented by 'x'.
Now, we know that the height of the left balloon is 48.2m and the height of the right balloon is 61.0m. The person in the left balloon observes that the right balloon is 13.3° above the horizontal.
To find the horizontal distance 'x', we need to find the length of the side adjacent to the angle of 13.3° in the right triangle we create.
We can use the tangent function, which relates the opposite side to the adjacent side in a right triangle. In this case, the opposite side is the height difference between the two balloons (61.0m - 48.2m = 12.8m) and the adjacent side is 'x'.
The tangent of an angle is given by:
tan(angle) = opposite/adjacent
So, we have:
tan(13.3°) = 12.8m/x
Rearranging the equation to solve for 'x', we get:
x = 12.8m / tan(13.3°)
Using a calculator, we can find the value of the tangent of 13.3° and substitute it into the equation to find the value of 'x'.