In triangle ABD, angle D = 90 degrees, sin B = √13 / 7, BD = 6. Find AB.

Given:
Given: right-angled triangle ABD;
angle D = 90;
sin B = √13 / 7;
BD = 6;
Find: AB -?
Solution:
1) Let’s use the formula
cos ^ 2B + sin ^ 2B = 1;
cos ^ 2B = 1 – sin ^ 2A;
cos ^ 2B = 1 – 13/49;
cos ^ 2B = 49/49 – 13/49;
cos ^ 2B = 36/49;
cos B = 6/7;
2) Consider a right-angled triangle ABD. The cosine of the angle in a right-angled triangle is equal to the ratio of the adjacent leg to the hypotenuse. Hence:
cos B = BD / AB;
AB = BD / cos A;
AB = 6: 6/7;
AB = 6 * 7/6;
AB = (6 * 7) / 6;
AB = (1 * 7) / 1;
AB = 7.
Answer: AB = 7.