Each leg of a compass is 10 cm long and has a angle between them. The points on which the compass's legs rest, how far apart are they?

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answer is B.

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Detailed Solution

Concept: Assume that points A and B serve as the compass's two legs. Assume that point C on the compass is the joint portion. Now, two sides of the triangle ABC will measure 10 cm, and the included angle will be

. To get the value of "c," use the cosine rule

. In the cosine formula above, "C" is the angle of

, and "a" and "b" are the sides that are perpendicular to angles A and B and have values of 10 cm each. The side "c" that has to have its value established is the one across from angle "C."
Question Image

The two legs of the compass are thought to rest on points A and B based on the illustration. Point C is believed to be the compass's junction point.
Now, if we represent a, b, and c as the sides that the angles A, B, and C are opposite of, we get

.
It is assumed that there is

angle between the compass's legs.
So,

.
Now, if we apply the cosine rule to the triangle above,

, we obtain

Putting

By cross multiplying,

Square roots on both sides, give us

.
Hence, option 2 is correct.

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