Find sinA to the nearest hundreths

side a=7 and side b=5

To find sinA, we need to use the trigonometric ratio of sine, which is defined as the ratio of the length of the side opposite angle A to the length of the hypotenuse of the right triangle.

In this case, side a is given as 7 and side b is given as 5. To find the length of the side opposite angle A, we can use the Pythagorean theorem:

c^2 = a^2 + b^2

where c is the length of the hypotenuse. Substituting the given values:

c^2 = 7^2 + 5^2
c^2 = 49 + 25
c^2 = 74

Taking the square root of both sides, we find:

c ≈ √74
c ≈ 8.60 (rounded to two decimal places)

Now that we know the length of the hypotenuse, we can find sinA using the sine ratio:

sinA = opposite/hypotenuse

In this case, the opposite side is 5 and the hypotenuse is approximately 8.60. Substituting these values:

sinA = 5/8.60
sinA ≈ 0.581 (rounded to three decimal places)

Therefore, sinA is approximately 0.581 to the nearest hundredth.