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1) the diagram shows equilateral triangle abc sharing a side with square abcde. the square has side lengths of 4. what is the length of line be? justify your answer. (in image)

2) *in image*

1) The length of BE ≅ 7.73

2) The beam clear the wires in its way to standing up straight because the length of the wire less than the height of the wires by 0.332

Step-by-step explanation:

Figure 1:

∵ The equilateral Δ share the side of the square

∵ The length of the side of the square = 4

∴ The length of the side of the Δ = 4

In Δ EAB:

∵ AE = 4 and AB = 4

∵ m∠A = 90 + 60 = 150°

By using cos Rule:

∵ (BE)² = (AE)² + (AB)² - 2(AE)(AB)cosA

∴ (BE)² = (4)² + (4)² - 2(4)(4)cos150 = 59.71281

∴ BE = 7.7274 ≅ 7.73

Figure 2:

∵ The beam makes ∠40° with the ground

∵ The top of the beam is above ground by 8 ft

∴ The length of the beam = 8/sin(40) = 12.446

∵ The beam makes ∠60° with the ground

∵ The length of the beam = 12.44579

∴ The height of the top of the beam from the ground

   = 12.44579 × sin(60) = 10.77837

∵ The height between the top of the beam and the wires in this

   position is 2

∴ The height of the wires from the ground = 10.778 + 2 = 12.778

∵ The length of the beam = 12.446

∴ 12.446 < 12.778

∴ The beam clear the wires in its way to standing up straight

circle area = pi * radius^2

if diameter = 10 then radius = 5

circle area = pi * 5^2

circle area = pi * 25

circle area = 78.5398163397 square units

step-by-step explanation:

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west