# In a triangle ABC, the angle is C = 90 AB = 12 AC = 5. Find the sine and tangent of A.

Given: right-angled triangle ABC;

angle C = 90;

AB = 12;

AC = 5.

Find: sin A and tg A -?

Solution:

1) Consider a right-angled triangle ABC.

By the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):

AC ^ 2 + BC ^ 2 = AB ^ 2;

5 ^ 2 + BC ^ 2 = 12 ^ 2;

25 + BC ^ 2 = 144;

BC ^ 2 = 144 – 25;

BC ^ 2 = 119;

BC = √119;

2. The sine of the angle in a right-angled triangle is equal to the ratio of the opposite leg to the hypotenuse. Hence:

sin A = BC / AB;

sin A = √119 / 12.

3.tg A = BC / AC;

tg А = √119 / 5.

Answer: sin A = √119 / 12; tg А = √119 / 5.

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