Jack N.

asked • 11/14/15

Hi. Please help me with the following mathematical question.

1) A flying doctor plane flies from its base (B), in a direction of 072degreesT for 80km to reach an outback station (S). From there, the flying doctor travels in a direction 162degreesT for 160km to reach a hospital (H).

a) Draw a labelled diagram showing the different positions of B, S and H and their earnings and all known distances (If you can) :).

b) How far is the hospital from the base?

c) What is the true bearing from the hospital to the base?

Thanks so much!!

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Inactive Tutor answered • 11/14/15

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Mark: Check ∠BSH
 
 
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Inactive Tutor

I am looking at my diagram. A bearing of 162° makes a angle of 18° with the North-South. This added to the 70° created by the first leg (by alternate interior angles) equals 88°.
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11/15/15

Inactive Tutor

The initial angle is 072, not 070, so the triangle is a right triangle.
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11/15/15

Inactive Tutor

Thank you for the correction. And how would you solve the problem?
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11/15/15

Inactive Tutor

Mark:
 
As you noted, 162 degrees is 18 degrees west of south and by vertical angles at S, the remaining portion of angle S is 72 degrees.  So angle B is 90 degrees.  We are dealing with a right triangle.  Now, it is simpler than laws of cosines or sines.
 
Side BS is 80 and side SH is 160.  This is in the ratio of 1:2, which corresponds to a 1:2:√3 triangle.  Thus, it is a 30, 60, 90 degree triangle, with angle B = 60 degrees.  Thus, the angle to H is 72+60=132 degrees.
 
Check me to make sure that is right.
 
Bob
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11/15/15

Inactive Tutor answered • 11/14/15

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a) Draw the diagram and label!
 
∠BSH = 88°
 
b) Use Law of Cosines to determine BH
 
c) Use Law of Sines to determine ∠SBH
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Jack N.

Is this correct? Can you supply me with your answers so i can check if mine are correct. Thanks Mark.
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11/15/15

Jack N.

If you get to chance, i would really appreciate it if you could help me with 2 other questions. 
 
1) Solve the following equations using inverse operations.

i) 3x-7=7+x

ii) 3[(6x-2)/4 (Separate)+ 1 ] = 33

2) A cylindrical (cylinder) water tank of diameter 2.2m and height of 3m is full of water. The water flows out of the base into a rectangular prism 7m long and 3m wide.

a) Find the volume of the water in the cylindrical water tank in:
i) cubic metres
ii) litres 

b) Let the height of the rectangular prism be hm. Find the volume of the rectangular prism (box) in terms of h. Do this by writing the formula for the volume of a rectangular prism and substituting in the two known values and h.

c) What would the minimum height (h, to the nearest cm) of the rectangular prism have to be if it is to hold all the water. 

Thanks so much!!
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11/15/15

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