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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
  • e)
    none of these
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
CD = (BD - BC) = It is given that the distance CD is covered in 10 seconds.
i.e., the distance 100(√3−1) is covered in 10 seconds.
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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 tower is 50 meters tall, how far is the boat from the tower?

To solve this problem, we can use trigonometry.

Let's assume that the distance between the man and the boat is x meters.

We know that the angle of depression is 45 degrees, which means that the angle between the horizontal line and the line of sight is also 45 degrees. Therefore, we can form a right triangle with the tower as the vertical side, the distance between the man and the boat as the horizontal side, and the hypotenuse as the line of sight.

Let's label the vertical side as 50 meters, the horizontal side as x meters, and the hypotenuse as h meters.

By using trigonometric ratios, we can determine the relationship between these sides:

In a right triangle, the tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

In this case, the tangent of the angle of depression is equal to the ratio of the length of the vertical side (50 meters) to the length of the horizontal side (x meters).

So, tan(45°) = 50/x

We know that tan(45°) = 1, so we can simplify the equation:

1 = 50/x

To solve for x, we can multiply both sides of the equation by x:

x = 50 meters

Therefore, the boat is 50 meters away from 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/hre)none of theseCorrect 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/hre)none of theseCorrect 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/hre)none of theseCorrect 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/hre)none of theseCorrect answer is option 'A'. Can you explain this answer?.
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