Question

The diagram below shows equilateral triangle ABC sharing a side with square ACDE. The square has side lengths of 4. What is BE? Justify your answer.

Answer 1

1. First, I will use trigonometry to find BE. To do that I will put a right angle right through the middle of the triangle and square. Since the triangle is an equilateral then I can drop a perpendicular and it will bisect the base of the figure. Since the sides are four and the triangle is split in the middle by a right angle which is 90 degrees and the corner on the left is 60 degrees and the other corner up to be 30 degrees, I need to find what is x in the middle of the equilateral triangle. So I would do sin 60 = opposite/hypotenuse, sin 60 = x/ 4, x = 4 sin(60), x = 3.46410161514. Then the next step is to find the total height of the triangle. The triangle sides and the square sides are all four and I need to find x in the middle of the triangle the x in the triangle is 3.46. To get the total height of the square I will do 4 + 3.46410161514 =7.46410161514, so the total height of the triangle is 7.46. Since the triangle is perpendicular because I put a right angle in the middle of the figure, then the square bottom is divided into two since it is four to get so it's two and two. So to get BE I will do tan A = 7.46410161514 / 2, then tan A= 3.7320508075, and then I will do tan^-1= 3.7320508075, so BE = 75 degrees.

Answer 2

is that the correct answer

Answer 3

we need to find the length of side BE . BE is not an angle

Answer 4

sides AB and AE are both equal to 4 and angle BAE = 90 + 60 = 150 degrees

Are you familiar with the Cosine rule? We can apply it to triangle ABE and find length of BE.

Answer 5

yes

Answer 6

Ok so BE^2 = 4^2 + 4^2 - 2*4*4 cos 150

Answer 7

ella posted this question a few days ago.
her work here is ok, but she found angle BED
and she can use trig to now find the length of the hypotenuse BE

Answer 8

9.62397419269 = BE^2

Answer 9

yes - I see what she has done now.

Answer 10

i dont get that

BE^2 = 32 - 32 cos 150

Answer 11

and cos 150 = -0.866

Answer 12

16+16-32=9.62.
9.62 cos 150 = 6.73

Answer 13

No ell thats is not the way to calculate it

we have a mixture of subtracts and multiplys here The Multiplication must be done ffirst

Answer 14

okay i get because 32- 32= 0 so u just do cos150

Answer 15

cos 150 =-0.86602540378

Answer 16

so 32 - 32* cos 150
= 32 - 32 * -0.866

the multiplication is done next:- ( -32* -0.866 = 27.712)
so we have
BE^2 = 32 + 27.712 = 59. 712

BE = sqrt 59.712

Answer 17

you can remember the order of operations using PEMDAS

Parentheses Exponents Multiply Divide Add Subtract

- that is the order in which they are done.

Answer 18

59.712= 32 - 32 * -0.866