Answer:
Explanation:
This is a problem involving a right triangle, where one angle is a 90-degree angle (denoted by the letter C). The problem provides the length of one side (b = 6) and the measure of one angle (A = 47 degrees). The goal is to find the length of the hypotenuse (c) of the triangle, which is the side opposite the right angle.
To solve this problem, we can use the trigonometric ratio known as the sine function. Specifically, we can use the sine of angle A to find the ratio of the length of the side opposite angle A (which is c) to the length of the hypotenuse (which is also c). This ratio is given by:
sin(A) = opposite/hypotenuse
Rearranging this formula, we can solve for c:
c = opposite/sin(A)
In this case, we know that the opposite side is c and the angle A is 47 degrees. To use the sine function, we need to convert the angle measurement to radians. We can do this by multiplying by pi/180, since there are pi radians in 180 degrees. So:
c = opposite/sin(A) = c/sin(47*pi/180)
Using a calculator to evaluate sin(47*pi/180), we get:
sin(47*pi/180) ≈ 0.7314
Substituting this value into the formula for c, we get:
c ≈ 6/0.7314 ≈ 8.20
Therefore, the length of the hypotenuse (c) is approximately 8.20 units, rounded to the nearest hundredth.