(GEOMETRY)Lian is making a banner for the school gym. She cut three pieces of fabric into congruent isosceles triangles, as shown.

Trigonometric area formula: Area = 1/2absin(c)

To the nearest square inch, how much fabric will she use to make all three triangles?

139 square inches

172 square inches

417 square inches

515 square inches

It is seen in the figure given that there are three triangles with sides equal to a = 17 inches, b = 17 inches, and c = 20.5. Our angle c is the angle opposite side c and that is 74°. Using the equation given in the question,
A of triangle = ((17 in)(17 in)(sin 74°))(1/2)
= 138.9 in²
Then, we multiply this area by 3 since there are 3 triangles.
total area = (138.9 in²)(3) = 416.7 in²
The area of the figure is most approximately equal to 417 in².

ayoushivt ayoushivt · Answer 2 · 2022-07-04T08:42:36+02:00

The total fabric that will be needed is 417 in², Option C is the answer.

What is a Triangle ?

A triangle is a polygon with three sides , angles and vertices.

It is given that

The two sides of the triangle is 20.5 in. and 17 in. and the angle C is 74 degree.

It is been asked to calculate the total fabric that will be needed ,

= 3 * Area of 1 triangle

Area of Triangle = 1/2absin(c)

Area of triangle = (1/2)(17 in)(17 in)(sin 74°)

= 139 sq. in

Total Area = 3 * 139 sq. in

= 416.7 in²

The total fabric that will be needed is 417 in².

To know more about Triangle

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