Answer:
To find which angle is bigger, A or B, we can use trigonometric ratios or the Pythagorean theorem.
Method 1: Trigonometric ratios
We can use the trigonometric ratios of sine and cosine to find the values of sin A and sin B, and then compare them to see which angle is bigger.
sin A = BC/AB = 10/14 = 0.714
sin B = AC/AB = √(AB^2 - BC^2)/AB = √(196 - 100)/14 = √96/14 = 0.707
cos A = AC/AB = √(AB^2 - BC^2)/AB = √(196 - 100)/14 = √96/14 = 0.707
cos B = BC/AB = 10/14 = 0.714
Since sin A > sin B and cos A < cos B, we can conclude that angle A is bigger than angle B.
Method 2: Pythagorean theorem
We can use the Pythagorean theorem to find the length of AC, and then use the ratios of the sides to find the values of sin A and sin B.
AC^2 = AB^2 - BC^2 = 196 - 100 = 96
AC = √96 = 9.8 cm
sin A = BC/AB = 10/14 = 0.714
sin B = AC/AB = 9.8/14 = 0.7
Since sin A > sin B, we can conclude that angle A is bigger than angle B.