# In triangle ABC, angle C = 90 degrees, Sin angle A = 4/5, AC = 9, find AB.

July 28, 2021 | education

| This problem can be solved in different ways.

The simplest is to use the property of the Egyptian triangle, as you can see the ratio of the leg and the hypotenuse is 4: 5 and one more leg is a multiple of 3 and is obtained by multiplying by 3. From this we can conclude that the hypotenuse AB is 5 * 3 = 15.

Another way is to use the basic trigonometric property to express the cosine of angle A and find AB.

Cos ^ 2A = 1 – 16/15 = AC ^ 2 / AB ^ 2.

AB ^ 2 = 81 * 25/9 = 225.

AB = 15.

Answer: AB = 15.

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