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A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 100 metres from the tower. After 10 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?
- a)26.28 km/hr
- b)32.42 km/hr
- c)24.22 km/hr
- d)31.25 km/hr
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A man is watching from the top of a tower a boat speeding away from th...
Consider the diagram shown above.
Let AB be the tower. Let C and D be the positions of the boat
Then,
ACB = 45° , 
ADC = 30°, BC = 100 m
(∵ Substituted the value of AB from equation 1)
=> BD =100√3
CD = (BD - BC) =(100√3−100)=100(√3−1)
It is given that the distance CD is covered in 10 seconds.
i.e., the distance 100(√3−1) is covered in 10 seconds.
CD = (BD - BC) =(100√3−100)=100(√3−1)
It is given that the distance CD is covered in 10 seconds.
i.e., the distance 100(√3−1) is covered in 10 seconds.
Most Upvoted Answer
A man is watching from the top of a tower a boat speeding away from th...
Degrees with the man's line of sight. If the height of the tower is 50 meters, how far is the boat from the base of the tower?
To solve this problem, we can use the tangent function, which relates the angle of depression to the opposite and adjacent sides of a right triangle.
Let's denote the distance from the base of the tower to the boat as x.
In the right triangle formed by the man, the tower, and the boat, the opposite side is the height of the tower (50 meters), and the adjacent side is the distance from the base of the tower to the boat (x meters).
According to the tangent function, the tangent of the angle of depression (45 degrees) is equal to the opposite side divided by the adjacent side:
tan(45) = opposite/adjacent
1 = 50/x
To find x, we can cross-multiply and solve for x:
x = 50/1
x = 50 meters
Therefore, the boat is 50 meters away from the base of the tower.
To solve this problem, we can use the tangent function, which relates the angle of depression to the opposite and adjacent sides of a right triangle.
Let's denote the distance from the base of the tower to the boat as x.
In the right triangle formed by the man, the tower, and the boat, the opposite side is the height of the tower (50 meters), and the adjacent side is the distance from the base of the tower to the boat (x meters).
According to the tangent function, the tangent of the angle of depression (45 degrees) is equal to the opposite side divided by the adjacent side:
tan(45) = opposite/adjacent
1 = 50/x
To find x, we can cross-multiply and solve for x:
x = 50/1
x = 50 meters
Therefore, the boat is 50 meters away from the base of the tower.
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A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 100 metres from the tower. After 10 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?a)26.28 km/hrb)32.42 km/hrc)24.22 km/hrd)31.25 km/hrCorrect answer is option 'A'. Can you explain this answer?
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A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 100 metres from the tower. After 10 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?a)26.28 km/hrb)32.42 km/hrc)24.22 km/hrd)31.25 km/hrCorrect answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 100 metres from the tower. After 10 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?a)26.28 km/hrb)32.42 km/hrc)24.22 km/hrd)31.25 km/hrCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 100 metres from the tower. After 10 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?a)26.28 km/hrb)32.42 km/hrc)24.22 km/hrd)31.25 km/hrCorrect answer is option 'A'. Can you explain this answer?.
A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 100 metres from the tower. After 10 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?a)26.28 km/hrb)32.42 km/hrc)24.22 km/hrd)31.25 km/hrCorrect answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 100 metres from the tower. After 10 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?a)26.28 km/hrb)32.42 km/hrc)24.22 km/hrd)31.25 km/hrCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of 45° with the man's eye when at a distance of 100 metres from the tower. After 10 seconds, the angle of depression becomes 30°. What is the approximate speed of the boat, assuming that it is running in still water?a)26.28 km/hrb)32.42 km/hrc)24.22 km/hrd)31.25 km/hrCorrect answer is option 'A'. Can you explain this answer?.
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