Question

A construction crew wants to hoist a heavy beam so that it is standing up straight. They tie a rope to the beam, secure the base, and pull the rope through a pulley to raise one end of the beam from the ground. When the beam makes an angle of 408 with the ground, the top of the beam is 8 ft above the ground.
The construction site has some telephone wires crossing it. The workers are concerned that the beam may hit the wires. When the beam makes an angle of 608 with the ground, the wires are 2 ft above the top of the beam. Will the beam clear the wires on its way to standing up straight? Exp

Answer 1

1. So first I need to find the length of the beam and I can do that by using trigonometry. So I will use Sin = opposite/ hypotenuse to find the length of the beam , so I will do sin 40 = x/8, sin 40/1=x/8, x = 8/sin(40), x= 12.4457906. So the length of the beam is 12.45. Then you will do it by 60 degree to see if it will touch the other wires by doing sin 60 = x / 12.45, sin60 / 1 = x / 12.45, x= 12.45 sin(60), so x = 10.7820162771. Because the beam is 12.45 ft. long it will not touch the wire since the wires are 10.78 ft. in the air.

Answer 2

it that the corect answer

Answer 3

***so I will do sin 40 = x/8, ***
you mean
sin 40 = 8/x
if we "flip" both sides , we get
1/sin 40 = x/8
and multiply both sides by 8 to get
8/sin40= x

you got that equation, but you did something peculiar or made a typo.
because if you use
sin 40 = x/8 and multiply both sides by 8, you get
8 sin40 = x (which is not what you want)

Answer 4

the rest of your work is good, and that is the correct answer

Answer 5

x = 8/sin(40) is correct

what you wrote that is wrong is
sin(40)= x/8
... and if you managed to get the correct equation x = 8/sin(40)
from sin(40) = x/8, then your algebra was wrong