contestada

A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate, as shown. The napkin has a perimeter of 38 centimeters.

Isosceles triangle A B C is shown. The length of A C is 8 centimeters and the lengths of sides A B and B C are congruent. Side A B has length c and side B C has length a. Angle A B C is 30 degrees.

Trigonometric area formula: Area = One-half a b sine (C)

To the nearest square centimeter, how many square centimeters of the plate are covered by the napkin?

16 square centimeters
30 square centimeters
56 square centimeters
60 square centimeters

Respuesta :

ajeigbeibraheem

The napkin covered approximately 56 square centimeters of the plate. The third option is correct.

What is the area of an isosceles triangle?

The area of an isosceles triangle can be estimated by using the trigonometric function:

[tex]\mathbf{=\dfrac{1}{2} \times a \times b\times sin (C)}[/tex]

From the given information:

  • The base angle and sides of an Isosceles triangle are equal.

The perimeter of the triangle:

P = a + b + c

38 = a + 8 + c

where;

  • a = c  (base  sides)

So;

38 = 8 + 2a

38 - 8 = 2a

2a = 30

a = c = 15

Similarly, ∠ABC = 30

∠A + ∠B + ∠C = 180   (sum of angles in a triangle)

∠A + 30 + ∠C = 180

∠A = ∠C = x

2x = 180 - 30

2x = 150

x = 150/2

∠A = ∠C = x  = 75°

Using the trigonometric function:

[tex]\mathbf{=\dfrac{1}{2} \times (15) \times (8) \times sin (75)}[/tex]

= 56 square centimeters.

Learn more about calculating the area of the triangle here:

https://brainly.com/question/23945265

#SPJ1

Otras preguntas