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A vertically straight tree, 15 m high, is broken by the wind in such a way that it's top just touches the ground and makes an angle of 60 with the ground. At what height from the ground did the tree break?
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Problem:
A vertically straight tree, 15 m high, is broken by the wind in such a way that its top just touches the ground and makes an angle of 60° with the ground. At what height from the ground did the tree break?
Solution:
To solve this problem, we can use trigonometry and create a right triangle with the tree as one side, the height from the ground to the break point as the hypotenuse, and the distance from the break point to the base of the tree as the other side.
Step 1: Identify the Given Information
We are given:
- The height of the tree is 15 m.
- The angle between the top of the tree and the ground is 60°.
Step 2: Identify the Unknown
We need to find the height from the ground to the break point of the tree.
Step 3: Set up the Trigonometric Equation
Let's denote the height from the ground to the break point as x meters. We can set up the following equation using the trigonometric relationship in a right triangle:
tan(60°) = x / 15
Step 4: Solve the Equation
To find x, we can solve the equation for x:
tan(60°) = x / 15
√3 = x / 15
x = 15√3
Step 5: Calculate the Height from the Ground to the Break Point
Using a calculator, we can evaluate the value of x:
x ≈ 15 * 1.732
x ≈ 25.98
Therefore, the height from the ground to the break point of the tree is approximately 25.98 meters.
A vertically straight tree, 15 m high, is broken by the wind in such a way that its top just touches the ground and makes an angle of 60° with the ground. At what height from the ground did the tree break?
Solution:
To solve this problem, we can use trigonometry and create a right triangle with the tree as one side, the height from the ground to the break point as the hypotenuse, and the distance from the break point to the base of the tree as the other side.
Step 1: Identify the Given Information
We are given:
- The height of the tree is 15 m.
- The angle between the top of the tree and the ground is 60°.
Step 2: Identify the Unknown
We need to find the height from the ground to the break point of the tree.
Step 3: Set up the Trigonometric Equation
Let's denote the height from the ground to the break point as x meters. We can set up the following equation using the trigonometric relationship in a right triangle:
tan(60°) = x / 15
Step 4: Solve the Equation
To find x, we can solve the equation for x:
tan(60°) = x / 15
√3 = x / 15
x = 15√3
Step 5: Calculate the Height from the Ground to the Break Point
Using a calculator, we can evaluate the value of x:
x ≈ 15 * 1.732
x ≈ 25.98
Therefore, the height from the ground to the break point of the tree is approximately 25.98 meters.
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A vertically straight tree, 15 m high, is broken by the wind in such a way that it's top just touches the ground and makes an angle of 60 with the ground. At what height from the ground did the tree break?
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A vertically straight tree, 15 m high, is broken by the wind in such a way that it's top just touches the ground and makes an angle of 60 with the ground. At what height from the ground did the tree break? 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 vertically straight tree, 15 m high, is broken by the wind in such a way that it's top just touches the ground and makes an angle of 60 with the ground. At what height from the ground did the tree break? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vertically straight tree, 15 m high, is broken by the wind in such a way that it's top just touches the ground and makes an angle of 60 with the ground. At what height from the ground did the tree break?.
A vertically straight tree, 15 m high, is broken by the wind in such a way that it's top just touches the ground and makes an angle of 60 with the ground. At what height from the ground did the tree break? 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 vertically straight tree, 15 m high, is broken by the wind in such a way that it's top just touches the ground and makes an angle of 60 with the ground. At what height from the ground did the tree break? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vertically straight tree, 15 m high, is broken by the wind in such a way that it's top just touches the ground and makes an angle of 60 with the ground. At what height from the ground did the tree break?.
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