Two men, 400 feet apart, observe a balloon between them; it is in the same vertical plane as they are. The respective angles of
elevation of the balloon are observed by the men to be 75°20' and 49°30'. Find x rounded to the nearest whole number.
2 answers:
Because x is not defined, it is assumed to be the height of the balloon.
Note that
75° 20' = 75.333°
49° 30' = 49.5°
From the figure shown below, obtain by definition,
a = x cot 49.5° = 0.8541x
b = x cot 75.333° = 0.2617x
Because a + b = 400 ft, therefore
0.8541x + 0.2617x = 400
1.1158x = 400
x = 358.49 ft
Answer: 358 ft (nearest whole number)
Note that
75° 20' = 75.333°
49° 30' = 49.5°
From the figure shown below, obtain by definition,
a = x cot 49.5° = 0.8541x
b = x cot 75.333° = 0.2617x
Because a + b = 400 ft, therefore
0.8541x + 0.2617x = 400
1.1158x = 400
x = 358.49 ft
Answer: 358 ft (nearest whole number)
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Answer:
≈ 82 feet
Step-by-step explanation:
Since the triangle is right use Pythagoras' identity to calculate distance (d)
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
Here the hypotenuse is the distance (d) between the 2 poles, hence
d² = 80² + 45² = 6400 + 2025 = 8425 ( take the square root of both sides )
d = ≈ 82 feet ( to the nearest foot )