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In triangle ABC, angle B is π/3 and angle C is π/4. If point D lies on BC and divides it internally in the ratio 1:3, what is the value of sin∠BAD divided by sin∠CAD?

1. 1/√6
2. 1/3
3. 1/√3
4. √2/3

Correct answer: 1/√6

Solution

The ratio of the sines of the angles ∠BAD and ∠CAD can be determined using the Law of Sines and the internal division of segment BC by point D. Given the angles of triangle ABC, the sine values can be calculated, leading to the conclusion that sin∠BAD/sin∠CAD equals 1/√6.

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