In a triangle ABC, the angle is C = 90 AB = 12 AC = 5. Find the sine and tangent of A.
September 30, 2021 | education
| 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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