Math Question Help!!!!!!!?

Question

In right triangle ABC with right angle C, AB=12 an AC=7 A.Find the length of side BC B.State the six trigonometric functions of angle A

Answer 1

Triangle ABC with right angle C .

Draw the triangle with right angle at C .

Using the Pythagoras theory of right angles .

(AB)² = (AC)² + (BC)²

12² = 7² + (BC)²

(BC)² = 12² - 7² 

(BC)² = 144 - 49

(BC)² = 95

BC = 9.74

So  the length of side BC is 9.74 .

Now find the six trigonometric functions at angle A 

sin ϴ = opposite side / hypotenuse 

sin ϴ = 9.74 / 12

sin ϴ = 0.812

cos ϴ = adjacent side / hypotenuse 

cos ϴ = 7 / 12

cos ϴ = 0.583

tan ϴ = opposite side / adjacent side 

tan ϴ = 9.74 / 7

tan ϴ = 1.392 

cosec ϴ = 1 / sin ϴ

cosec ϴ = 1 / 0.812

cosec ϴ = 1.231

sec ϴ = 1 / cos ϴ

sec ϴ = 1 / 0.583

sec ϴ = 1.715

cot ϴ = 1 / tan ϴ 

cot ϴ = 1 / 1.392 

cot ϴ = 0.718

Now tabulate six trigonometric functions at angle A .

S.No	Trigonometric function	Value
1	sin ϴ	0.812
2	cos ϴ	0.583
3	tan ϴ	1.392
4	cosec ϴ	1.231
5	sec ϴ	1.715
6	cot ϴ	0.718