Year 10 maths trigonometry problem help please ,cheers! ?

Question

A cable car is supported by two wires attached to a horizontal cable.

One of the wires is 5.4m long and makes an angle of 43 degrees and 20 minutes with the horizontal cable. the other wire makes an angle of 31 degrees and 45 minutes with the cable. How far apart along the cable are the wires , to 2 decimal places.

The answer was: 9.92 metres

My problem is i can't form the picture in my head , can someone please help show me the methods of how you got the answer! thanks so much .

Answer 1

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43deg 20 min = 43.33 deg

31 deg 45 min = 31.75 deg

180 - ( 43.33 + 31.75 ) = 104.92 deg

5.5 / sin 31.75  = x / sin 104.92

x = ( 5.4 * sin 104.92 ) / sin 31.75

x = 9.916 m = 9.92 m

x is how far apart along the cable are the wires , to 2 decimal places.

Answer 2

you draw an obtuse angled (104 deg 55 min) triangle vertex downward and base horizontal with sides making angles 43 deg 20 min and 31 deg 45 min.

then length of base = 5.4 cos(43deg20min) + 5.4sin(43deg20min)cot(31deg45min) = 9.92  

Answer 3

Ok, yer makin a triangle here

Draw a horizontal line, this is the moving cable

Attached to it, hanging down, are the car attaching cables

They both meet at the top center of the car, making a triangle with the base being up and it is the horizontal line

First is the one were you know the angle and hyp, you can solve for both the height of the triangle (used in the next calc) and the portion of the horizontal cable on that angles side

sine = opposite/hyp

sine (43'20"") = opposite/5.4

Opposite = 5.4 * 0.68624

=3.706

cos = adjacent /hyp

cos (43'20"") = horizontal port / 5.4

.727 * 5.4 = horizontal

3.928

Now calc the  other part of the horizontal

tan = opposite / adjacent

tan (31'45"") = 3.706 / adjacent

adjacent = 3.706 / 0.6188

adj = 5.989

So, add them together 3.928 and 5.989 and you get

9.917, this rounds to 9.92 m

Answer 4

draw a diagram. remeber cos sin and tan

Answer 5

If x = length of the second wire,

x = 5.4sin(43.33°)/sin(31.75°) = 7.04 m

Distance between the two wires

= 5.4cos(43.33°) + 7.04cos(31.75°)

= 3.93 + 5.99

= 9.92 m.