SOLUTION: Soil contractor Frank was given the following dimensions over the telephone. The triangular garden plot ABC has an angle CAB measuring 44 degrees, AC is 8m long and BC is 6m long.

Question 1026223: Soil contractor Frank was given the following dimensions over the telephone. The triangular garden plot ABC has an angle CAB measuring 44 degrees, AC is 8m long and BC is 6m long. Soil to a depth of 10cm is required.
I) Explain why Frank needs extra information from his client.
ii) What is the maximum volume of soil needed if his client is unable to supply the necessary information?
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
With the given information, I would
use Sine Rule to obtain Angle CBA
and then angle ACB.
a/SinA = b/SinB
6/Sin44 = 8/SinB
SinB = (8 x sin44)/6
SinB = 0.9262
Angle CBA = 67.9 degrees
Angle ACB = 180 -(44 + 67.9)
Angle ACB = 68.1 degrees.
Now using the area formula:
= 1/2(ab SinC)
= 1/2 x 8 x 6 x Sin 68.1
= 22.27 m^2 (Area)
Multiply by depth to obtain volume of soil.
= 22.27 x 0.1 = 2.227 m^3 (3 decimal places)
Hope this helps :-)
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