In triangle ABC, angle B is 90, BC = 6, AC = 10 Find sin C.

Given:

ABC – right triangle;

Angle B = 90 degrees;

BC = 6;

AC = 10;

Find sin c.

Solution:

1) First, find cos c.

In order to find the triangle ABC, we use the formula:

cos c = BC / AC.

Substitute the known values into the formula.

cos c = 6/10 = (2 * 3) / (2 * 5) = (1 * 3) / (1 * 5) = 3/5;

2) Find sin c from the formula sin ^ 2 c + cos ^ 2 c – 1;

sin c = √ (1 – cos ^ 2 c) = √ (1 – (3/5) ^ 2) = √ (1 – 9/25) = √ ((25 – 9) / 25 = √ (16/25 ) = √16 / √25 = 4/5;

As a result, we got sin c = 4/5.

Answer: sin c = 4/5.