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Explain Bot To find the height of the balloons, we can use trigonometry and the given angles. Let's break down the problem step by step:
Step 1: Draw a diagram
Draw a diagram with A and B representing the balloons, O representing the ground observation position, and X representing the point directly below the balloons on the ground.
Step 2: Calculate the distance from O to X
Since A and B are 1000 meters apart and X is directly below the balloons, the distance from O to X is also 1000 meters.
Step 3: Calculate the distance from A to X
To find the distance from A to X, we can use trigonometry. Given that angle AOX is 45 degrees 15 minutes, we can convert it to decimal degrees. 1 minute is equal to 1/60 of a degree, so 15 minutes is equivalent to 15/60 = 0.25 degrees.
Therefore, the angle AOX is 45.25 degrees. We can use the tangent function to calculate the distance from A to X.
tangent(angle AOX) = opposite/adjacent
tangent(45.25 degrees) = height of balloon A / distance from A to X
We can rearrange the equation to solve for the height of balloon A:
height of balloon A = distance from A to X * tangent(angle AOX)
Step 4: Calculate the distance from B to X
Using the same method as in Step 3, we can find the distance from B to X. Given that angle BOX is 10 degrees 30 minutes, we can convert it to decimal degrees. 30 minutes is equal to 30/60 = 0.5 degrees.
Therefore, the angle BOX is 10.5 degrees. Again, using the tangent function, we can calculate the distance from B to X.
tangent(angle BOX) = opposite/adjacent
tangent(10.5 degrees) = height of balloon B / distance from B to X
Rearranging the equation gives us:
height of balloon B = distance from B to X * tangent(angle BOX)
Step 5: Calculate the height of the balloons
Substitute the given values and calculate the height of each balloon separately using the formulas from Steps 3 and 4.
Once you have calculated the height of balloon A and balloon B, you will have your answer.
Salotte