In triangle ABC, angle C is 90 degrees, BC = 5√7, AB = 20. Find sin B.

Given:

ABC – right triangle,

AB – hypotenuse,

BC = 5√7 centimeters,

AB = 20 centimeters.

Find: sin B

Decision:

1) Consider a right-angled triangle ABC. By the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):

AC ^ 2 + BC ^ 2 = AB ^ 2:

AC ^ 2 + (5√7) ^ 2 = 20 ^ 2;

AC ^ 2 + 175 = 400;

AC ^ 2 = 400 – 175;

AC ^ 2 = 225;

AC = 15 centimeters.

2) Consider a right-angled triangle ABC. The sine of the angle in a right-angled triangle is equal to the ratio of the opposite leg to the hypotenuse. Hence:

sin B = AC / AB;

sin B = 15/20;

sin B = 3/4.

Answer: 3/4.