The length of the portion BC of the cloth is 6 sin 32
Please find attached an image of the triangle used in answering this question
The triangle is a right-angled triangle
A right-angled triangle is a triangle that has an angle that measures 90 degrees. Also, this type of triangle has a longest side which is called the hypotenuse
In this question, we are to find BC
We are given the value of the angle opposite BC. It is 32 degrees
We are given the length of the hypotenuse which is 6 inches
Remember the notation SOHCAHTOA
This means :
1. when given the opposite side and hypotenuse of the right-angled triangle, sine would be used to determine the angle
2. When given the adjacent side and the hypotenuse of the right-angled triangle, cosine would be used to determine the angle
3. When provided with the opposite side and the adjacent side of the right-angled triangle, tan would be used to determine the angle
Because we are to determine the length of the side opposite the given angle and we are also provided with the hypotenuse, Sin would be used
Sine = opposite / hypotenuse
sin 32 = BC / 6
Cross multiply
6 x sin 32 = BC
In order to determine the length BC, make use of Sin which opposite divided by hypotenuse
You can find more information on how to determine the missing length of a right-angled triangle using Sin here : https://brainly.com/question/15551961?referrer=searchResults
