Reduced ratio 27 to 9
1 answer:
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Answer:
Width of the Rectangular Tin=8 inch
Length of the Rectangular Tin= 16 inch
Step-by-step explanation:
Let the Width of the Rectangle=W
The length of the piece of tin is twice the width, Length = 2W
Since Squares of 3 inch are cut from all four corners of the rectangle
Length of the box = 2W-(3+3)=(2W-6) inches
Breadth of the Box = W-(3+3)=(W-6) inches
Height = 3 inches
Volume of the box = 60 cubic inches
Now, Volume of a cuboid=lbh
3(2W-6)(W-6)=60
Divide both sides by 3
(2W-6)(W-6)=20
Expanding the brackets
Factorizing
Since the Width cannot be less than 6,
Width of the Rectangular Tin=8 inch
Length= 2 X 8 = 16 inch
Answer:
Sine rule states that the ratio of a side of a triangle to the angle opposite the side is equivalent for all 3 sides and their respective opposite angles.
Thus, the side opposite ∠B is side AC, which is 10 units long. The side opposite ∠A is side BC, which is 8 units long. Substitute these values into the formula. (We are at line 2 of working)
Line 3: multiply both sides by 10 to find sinB
This would give us
This is can also be written as: (as seen in line 4)
To find the measure of angle B:
<em>~ Explanation for line 6 and onwards~</em>
The sine of an angle is positive in quadrants I and II. Since sinB is positive (≈0.69899), we are looking at these 2 quadrants. Since the reference angle is 44° rounded off to the nearest whole degree, in quadrant I, the angle would be 44° too.
In quadrant 2, the angle would be 180° -44°= 136°.