On a piece of paper draw and label a right triangle using the given sides, solve for the unknown side and write the trigonometric functions for angles A and B, if a=5 and c=7.
I already found side b which equals 2 sqrts of 6.
Now I need to find the sin A and cos A. I know that sin is opposite/hypotenuse and cos is adjacent / hypotenuse. That’s as far as I can get however, I am provided with choices;
Sin A
a)7/5
b)2sqrt6/7
c)7/2sqrt6
d)5/7
Cos A
a)7/5
b)7/2sqrt6
c)2sqrt6/7
d)5/7
Please help!!!
So why not use for sine the value of a/c, and for cosine, b/c ?
To find the sine and cosine of angle A, we can use the ratios of sides of the triangle. We have already found side b to be 2√6.
To find the sine of angle A, we use the ratio of the length of the side opposite angle A to the length of the hypotenuse. In this case, side a is opposite angle A, and side c is the hypotenuse. Therefore, sin A = a/c.
Substituting the given values, we have sin A = 5/7.
To find the cosine of angle A, we use the ratio of the length of the side adjacent to angle A to the length of the hypotenuse. In this case, side b is adjacent to angle A, and side c is the hypotenuse. Therefore, cos A = b/c.
Substituting the given values, we have cos A = (2√6)/7.
Now let's compare these values with the provided choices:
Sin A:
a) 7/5
b) 2√6/7
c) 7/2√6
d) 5/7
Cos A:
a) 7/5
b) 7/2√6
c) 2√6/7
d) 5/7
From the calculations above, we can see that the correct choices are:
Sin A: d) 5/7
Cos A: c) 2√6/7
So the correct values for sin A and cos A are 5/7 and 2√6/7, respectively.