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A parachutist is descending vertically. At a certain height , his angle of elevation from a point on the ground is 60 degree and when he descended 300m further, the angle of elevation becomes 45 degree from the same point of observation. Find the distance of the point of observation from the place where the parachutist lands?
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A parachutist is descending vertically. At a certain height , his angl...
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A parachutist is descending vertically. At a certain height , his angl...
Given:
- Angle of elevation from a point on the ground at a certain height is 60 degrees.
- Angle of elevation from the same point of observation, when the parachutist descended 300m further, is 45 degrees.
To Find:
- The distance of the point of observation from the place where the parachutist lands.
Assumptions:
- The ground is horizontal.
- The parachutist is descending vertically.
Let's solve the problem step by step:
Step 1: Let's assume the initial height of the parachutist from the ground is 'h' meters.
Step 2: Using trigonometry, we can determine the distance (x) of the point of observation from the place where the parachutist lands.
- From the given information, we can form a right-angled triangle with the parachutist, the point of observation, and the place where the parachutist lands.
- The angle of elevation of 60 degrees gives us the opposite side as 'h' meters and the adjacent side as 'x' meters.
- Similarly, the angle of elevation of 45 degrees gives us the opposite side as 'h - 300' meters and the adjacent side as 'x' meters.
Step 3: Using the trigonometric ratios of sine and tangent, we can form equations to solve for 'x'.
- For the angle of elevation of 60 degrees:
- sin(60) = h / x
- x = h / sin(60)
- For the angle of elevation of 45 degrees:
- tan(45) = (h - 300) / x
- x = (h - 300) / tan(45)
Step 4: Equating the two values of 'x' obtained from Step 3:
h / sin(60) = (h - 300) / tan(45)
Step 5: Simplifying and solving the equation:
- Multiplying both sides by sin(60) and tan(45):
h * tan(45) = (h - 300) * sin(60)
- Simplifying further:
h * (1 / 1) = (h - 300) * (√3 / 1)
h = h√3 - 300√3
- Rearranging the equation:
h - h√3 = -300√3
h(1 - √3) = -300√3
- Dividing both sides by (1 - √3):
h = -300√3 / (1 - √3)
Step 6: Calculating the value of 'h':
h ≈ -300√3 / (1 - √3) ≈ 437.67 meters
Step 7: Calculating the distance 'x' of the point of observation:
x = h / sin(60)
x ≈ 437.67 / sin(60) ≈ 502.82 meters
Therefore, the distance of the point of observation from the place where the parachutist lands is approximately 502.82 meters.
- Angle of elevation from a point on the ground at a certain height is 60 degrees.
- Angle of elevation from the same point of observation, when the parachutist descended 300m further, is 45 degrees.
To Find:
- The distance of the point of observation from the place where the parachutist lands.
Assumptions:
- The ground is horizontal.
- The parachutist is descending vertically.
Let's solve the problem step by step:
Step 1: Let's assume the initial height of the parachutist from the ground is 'h' meters.
Step 2: Using trigonometry, we can determine the distance (x) of the point of observation from the place where the parachutist lands.
- From the given information, we can form a right-angled triangle with the parachutist, the point of observation, and the place where the parachutist lands.
- The angle of elevation of 60 degrees gives us the opposite side as 'h' meters and the adjacent side as 'x' meters.
- Similarly, the angle of elevation of 45 degrees gives us the opposite side as 'h - 300' meters and the adjacent side as 'x' meters.
Step 3: Using the trigonometric ratios of sine and tangent, we can form equations to solve for 'x'.
- For the angle of elevation of 60 degrees:
- sin(60) = h / x
- x = h / sin(60)
- For the angle of elevation of 45 degrees:
- tan(45) = (h - 300) / x
- x = (h - 300) / tan(45)
Step 4: Equating the two values of 'x' obtained from Step 3:
h / sin(60) = (h - 300) / tan(45)
Step 5: Simplifying and solving the equation:
- Multiplying both sides by sin(60) and tan(45):
h * tan(45) = (h - 300) * sin(60)
- Simplifying further:
h * (1 / 1) = (h - 300) * (√3 / 1)
h = h√3 - 300√3
- Rearranging the equation:
h - h√3 = -300√3
h(1 - √3) = -300√3
- Dividing both sides by (1 - √3):
h = -300√3 / (1 - √3)
Step 6: Calculating the value of 'h':
h ≈ -300√3 / (1 - √3) ≈ 437.67 meters
Step 7: Calculating the distance 'x' of the point of observation:
x = h / sin(60)
x ≈ 437.67 / sin(60) ≈ 502.82 meters
Therefore, the distance of the point of observation from the place where the parachutist lands is approximately 502.82 meters.
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A parachutist is descending vertically. At a certain height , his angle of elevation from a point on the ground is 60 degree and when he descended 300m further, the angle of elevation becomes 45 degree from the same point of observation. Find the distance of the point of observation from the place where the parachutist lands?
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A parachutist is descending vertically. At a certain height , his angle of elevation from a point on the ground is 60 degree and when he descended 300m further, the angle of elevation becomes 45 degree from the same point of observation. Find the distance of the point of observation from the place where the parachutist lands? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A parachutist is descending vertically. At a certain height , his angle of elevation from a point on the ground is 60 degree and when he descended 300m further, the angle of elevation becomes 45 degree from the same point of observation. Find the distance of the point of observation from the place where the parachutist lands? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A parachutist is descending vertically. At a certain height , his angle of elevation from a point on the ground is 60 degree and when he descended 300m further, the angle of elevation becomes 45 degree from the same point of observation. Find the distance of the point of observation from the place where the parachutist lands?.
A parachutist is descending vertically. At a certain height , his angle of elevation from a point on the ground is 60 degree and when he descended 300m further, the angle of elevation becomes 45 degree from the same point of observation. Find the distance of the point of observation from the place where the parachutist lands? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A parachutist is descending vertically. At a certain height , his angle of elevation from a point on the ground is 60 degree and when he descended 300m further, the angle of elevation becomes 45 degree from the same point of observation. Find the distance of the point of observation from the place where the parachutist lands? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A parachutist is descending vertically. At a certain height , his angle of elevation from a point on the ground is 60 degree and when he descended 300m further, the angle of elevation becomes 45 degree from the same point of observation. Find the distance of the point of observation from the place where the parachutist lands?.
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A parachutist is descending vertically. At a certain height , his angle of elevation from a point on the ground is 60 degree and when he descended 300m further, the angle of elevation becomes 45 degree from the same point of observation. Find the distance of the point of observation from the place where the parachutist lands?, a detailed solution for A parachutist is descending vertically. At a certain height , his angle of elevation from a point on the ground is 60 degree and when he descended 300m further, the angle of elevation becomes 45 degree from the same point of observation. Find the distance of the point of observation from the place where the parachutist lands? has been provided alongside types of A parachutist is descending vertically. At a certain height , his angle of elevation from a point on the ground is 60 degree and when he descended 300m further, the angle of elevation becomes 45 degree from the same point of observation. Find the distance of the point of observation from the place where the parachutist lands? theory, EduRev gives you an
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