The lengths of the sides of a rectangle are 12.4 and 26. What are the measures of the angles between its diagonals? Round your a
nswers to the nearest whole number.
1 answer:
Answer:
51°, 129°
Step-by-step explanation:
The ratio of the sides is the tangent of the angle a diagonal makes with the side of the rectangle. The smaller such angle will be
arctan(12.4/26) ≈ 25.5°
The smaller of the angles between the diagonals will be twice this value, or 51°. Its supplement is the larger angle between the diagonals, 129°.
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Answer:
The plates will not fit into the box.
Step-by-step explanation:
Each plate is 0.5 inches tall; therefore, the stack of 8 plates will have a height of .
Also, the diameter of the largest plate is 10 inches or has a radius of 5 inches, which matches the radius of the cylindrical box; therefore, we know that the stack of plates can fit into the base area of the cylindrical box.
What we want to figure out now is the height of the cylindrical box <em>to see if it is greater than or equal to 4 inches</em>—<em>the height of the stack of plates. </em>
The volume of a cylinder is , and since for our cylindrical box the volume is 150 cubic inches; therefore,
putting in and solving for height
we get
,
which is not greater than 4 inches, which means the plates will not fit into the box since the height of the stack is greater than the height of the box.