How do you find the base of a triangle if is not given?

Answer 1

You use trigonometry.

If the triangle is a right triangle, then you can use the Pythagorean theorem (a2 + b2 = c2 where c is the hypotenuse). This requires you to know two of the sides of the triangle.

You can also use the relationship:

sin A = a/c

cos A = b/c

tan A = a/b

where "A" is a non-right angle of a right triangle, "a" is the length of the side opposite of the angle "A", "b" is the length of the side adjacent to the angle "A" and "c" is the length of the hypotenuse.

If the triangle is NOT a right triangle, you can use the law of sines or the law of cosines.

The law of sines:

a /sin A = b / sin B = c / sin C

where "a" is the side opposite of angle "A", "b" is the side opposite of angle "B" and "c" is the side opposite of angle "C".

The law of cosines:

a2 = b2 + c2 - b*c*cos A

b2 = a2 + c2 - a*c*cos B

c2 = a2 + b2 - a*b*cos C

where "c" is the hypotenuse, "a" and "b" are the other sides of the triangle and "C" is the angle opposite of "c", "B" is the angle opposite of "b" and "A" is the angle opposite of "a".