Question

Express sin A,cos A and tan A as ratios

Answer 1

Part A)
`sin(A)=(2√(42))/(23)`

Part B)
`cos(A)=(19)/(23)`

Part C)
`tan(A)=(2√(42))/(19)`

Explanation:

Part A) we know that

In the right triangle ABC of the figure the sine of angle A is equal to divide the opposite side angle A by the hypotenuse

so

`sin(A)=(BC)/(AB)`

substitute the values

`sin(A)=(2√(42))/(23)`

Part B) we know that

In the right triangle ABC of the figure the cosine of angle A is equal to divide the adjacent side angle A by the hypotenuse

so

`cos(A)=(AC)/(AB)`

substitute the values

`cos(A)=(19)/(23)`

Part C) we know that

In the right triangle ABC of the figure the tangent of angle A is equal to divide the opposite side angle A by the adjacent side angle A

so

`tan(A)=(BC)/(AC)`

substitute the values

`tan(A)=(2√(42))/(19)`