# In triangle ABC, angle C is 90, AB = 12, sinA 3√11 / 10. Find AC

September 30, 2021 | education

| Given: right-angled triangle ABC;

angle C = 90;

sin A = 3√11 / 10;

AB = 12;

Find: AS -?

Solution:

1) Let’s use the formula

cos ^ 2A + sin ^ 2A = 1;

cos ^ 2A = 1 – sin ^ 2A;

cos ^ 2A = 1 – 9 * 11/100

cos ^ 2A = 100/100 – 99/100;

cos ^ 2A = 1/100;

cos A = 1/10;

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

cos A = AC / AB;

AC = AB * cos A;

AC = 12 * 1/10;

AC = 12/10;

AC = 1.2 centimeters.

Answer: 1.2 centimeters.

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