# In triangle ABC, angle C is 90, sin A = 0.3, AC = 6. Find AB.

September 28, 2021 | education

| In triangle ABC we find the hypotenuse AB.

It is known:

Angle C is 90 °;

sin A = 0.3;

AC = 6.

Solution:

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

cos A = AC / AB.

Hence, AB = AC / cos a;

Find cos a if the value of sin a is known.

cos a = √ (1 – sin ^ 2 a) = √ (1 – 0.3 ^ 2) = √ (1 – 0.09) = √0.81 = 0.9;

Substitute the known values into the formula and find the hypotenuse AB.

AB = 6 / 0.9 = 6 / (9/10) = 6 * 10/9 = 2 * 10/3 = 20/3;

Answer: AB = 20/3.

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