Answer :
Final answer:
To find the distance between the arms of a pair of dividers, use the Pythagorean theorem and cosine rule.
Explanation:
The distance between the arms of a pair of dividers can be found by using the Pythagorean theorem. Since we have the length of both arms and the angle between them, we can use the formula:
Distance = √(arm1² + arm2² - 2 * arm1 * arm2 * cos(angle))
Substituting the given values:
- arm1 = 9.8 cm
- arm2 = 9.8 cm
- angle = 62°
Distance = √(9.8² + 9.8² - 2 * 9.8 * 9.8 * cos(62°))
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Final answer:
To find the distance between the tips of the dividers, use the formula for the length of a chord, which is 2 * Radius * sin(Angle/2), where Radius is the length of one arm of the dividers (9.8 cm) and Angle is the angle between the arms (62 degrees).
Explanation:
In mathematics, you can solve this kind of problem using concepts from trigonometry. Specifically, you are given the length of a pair of dividers (which we can think of as a line segment) and the angle between the arms, and you're asked to find the distance between the tips of the dividers. That distance can be found using the formula for the length of a chord.
Here's how to do it step by step:
- First, you know that the length of the chord is given by: Length of chord = 2 * Radius * sin(Angle/2). In this case, the radius is simply the length of one arm of the dividers which is given as 9.8 cm.
- Second, the angle between the arms is given as 62 degrees. Plugging values into the formula, we get: Length of chord = 2 * 9.8 * sin(62/2).
- To get the final distance in cm, you need to evaluate this expression. Don't forget to make sure your calculator is set to degrees, not radians.
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