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(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

(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: A class=

Verified Answer :

taskmasters

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.

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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