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The figure below shows a triangular piece of cloth:

Triangle ABC has angle ABC equal to 90 degrees and angle BAC equal to 32 degrees. Length of AC is 6 inches.

What is the length of the portion BC of the cloth?

6 cos 32°
6 sin 32°
cos 32 degrees divided by 6
sin 32 degrees divided by 6

Sagot :

Answer:

6 sin 32

Step-by-step explanation:

sin∅ = opp/hyp

sin A = BC / AC

Plug in the givens

sin32 = BC / 6

multiply both sides by 6

6 sin 32 = BC

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

View image Ewomazinoade
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