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 Math Central Quandaries & Queries
 Question from Tracy, a student: I have a scalene triangle ABC, angle C is 20 degrees, side AC is 8cm and side AB is 3 cm. Line CB is extended to point D which is perpendicular to point A, triangle ABD is a right-angled triangle. How do I calculate length of line AD

Tracy,

The length of AB in triangle ABD is the same as the length AB in triangle ACD. Ignore piont B entirely. Thus ACD is a right triangle (the right angle is at point D, after all).

So you have a right triangle ACD, you know the length AC of the hypotenuse is 8, and the angle opposite AD is 20 degrees. Is there a trig function that involves the hypotenuse, one angle and the length of the side opposite to it? Yes, it is SINE.

Cheers,
Stephen La Rocque.

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