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A triangle can be drawn if the hypotenuse and a _____ in the case of a right-angled triangle.
- a)base
- b)hypotenuse
- c)leg
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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A triangle can be drawn if the hypotenuse and a _____ in the case of a...
Explanation:
A right-angled triangle is a triangle in which one of the angles is a right angle (90 degrees). The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs. To draw a triangle, you need at least three sides or two sides and an angle. In the case of a right-angled triangle, if you know the length of the hypotenuse and one leg, you can draw the triangle.
Why option C is correct:
The correct answer is option C, leg. This is because if you know the length of the hypotenuse and one leg, you can use the Pythagorean theorem to find the length of the other leg. The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. So, if you know the length of the hypotenuse (c) and one leg (a), you can find the length of the other leg (b) using the following formula:
b = √(c^2 - a^2)
Once you know the length of all three sides, you can draw the triangle.
Example:
Suppose you want to draw a right-angled triangle with a hypotenuse of length 5 units and one leg of length 3 units. To find the length of the other leg, you can use the Pythagorean theorem:
b = √(c^2 - a^2)
b = √(5^2 - 3^2)
b = √(25 - 9)
b = √16
b = 4
So, the length of the other leg is 4 units. Now that you know the length of all three sides, you can draw the triangle.
A right-angled triangle is a triangle in which one of the angles is a right angle (90 degrees). The side opposite to the right angle is called the hypotenuse, and the other two sides are called legs. To draw a triangle, you need at least three sides or two sides and an angle. In the case of a right-angled triangle, if you know the length of the hypotenuse and one leg, you can draw the triangle.
Why option C is correct:
The correct answer is option C, leg. This is because if you know the length of the hypotenuse and one leg, you can use the Pythagorean theorem to find the length of the other leg. The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. So, if you know the length of the hypotenuse (c) and one leg (a), you can find the length of the other leg (b) using the following formula:
b = √(c^2 - a^2)
Once you know the length of all three sides, you can draw the triangle.
Example:
Suppose you want to draw a right-angled triangle with a hypotenuse of length 5 units and one leg of length 3 units. To find the length of the other leg, you can use the Pythagorean theorem:
b = √(c^2 - a^2)
b = √(5^2 - 3^2)
b = √(25 - 9)
b = √16
b = 4
So, the length of the other leg is 4 units. Now that you know the length of all three sides, you can draw the triangle.
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