Betsy is in a hot air baloon 350 m above the ground. She observes her house at an angle of depression of 310 and the mall at an angle of depression of 430.1) Which building is farthest away from Betsy? Enter house or mall in lower case letters.2) How far is the farthest building on the ground directly below Betsy?Round you answer to the nearest WHOLE number. Enter only numbers and no units in the box.3) How far is the closest building to a point on the ground directly under Betsy?Round you answer to the nearest WHOLE number. Enter only numbers and no units in the box.
Question
Betsy is in a hot air baloon 350 m above the ground. She observes her house at an angle of depression of 310 and the mall at an angle of depression of 430.1) Which building is farthest away from Betsy? Enter house or mall in lower case letters.2) How far is the farthest building on the ground directly below Betsy?Round you answer to the nearest WHOLE number. Enter only numbers and no units in the box.3) How far is the closest building to a point on the ground directly under Betsy?Round you answer to the nearest WHOLE number. Enter only numbers and no units in the box.
Solution
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The building that is farthest away from Betsy is the house. This is because the angle of depression to the house is smaller, meaning that the house is at a steeper angle and therefore further away.
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To find the distance to the farthest building (the house), we can use the tangent of the angle of depression, which is the height divided by the distance. So, the distance is the height divided by the tangent of the angle.
Distance to the house = 350m / tan(31) = 611.7m. Rounded to the nearest whole number, this is 612m.
- Similarly, to find the distance to the closest building (the mall), we use the same formula.
Distance to the mall = 350m / tan(43) = 334.4m. Rounded to the nearest whole number, this is 334m.
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