if a=6 in. and θ=45 degree, find the value of c. round you answer to the nearest hundreth
Based on the given information, we can use the sine function to find the value of c.
Recall that the sine function is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.
In this case, the side opposite angle θ is a, and the hypotenuse is c.
Using the given information, we have:
sin(θ) = opposite/hypotenuse
sin(45°) = a/c
sin(45°) = 6/c
We can solve for c by rearranging the equation:
c * sin(45°) = 6
c = 6 / sin(45°)
Using a calculator, sin(45°) is approximately 0.7071.
c ≈ 6 / 0.7071 ≈ 8.49
Therefore, the value of c rounded to the nearest hundredth is approximately 8.49.