In triangle ABC, angle C = 90 degrees sine A = 0.8, AC = 6 find AB.

Take a triangle ABC with legs AC and BC, right angle C = 90 ° and hypotenuse AB. It is known that the length of the leg AC is 6:

| AC | = 6;

and the sine of angle A is 0.6:

sin (∠A) = 0.6;

Using identity:

cos2 (∠A) + sin2 (∠A) = 1;

we calculate further cos (∠A):

cos (∠A) = √ (1 – sin2 (∠A)) = √ (1 – (0.8) 2 = 0.6;

To calculate | AB | we will use the fact that the cosine of the angle is equal to the ratio of the length of the adjacent leg to the length of the hypotenuse:

cos (∠A) = | AC | / | AB |;

We get:

0.6 = 6 / | AB |;

| AB | = 6 / 0.6 = 10;

Answer: | AB | = 10