Is this statement true or false?
2 answers:
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Answer:
Step-by-step explanation:
We have been given that Wren’s first display box is 6 inches long, 9 inches wide, and 4 inches high. We are asked to find the volume of display box.
We know that the box is in form of cuboid, so its volume would be length times width times height.
Therefore, the volume of the display box is 216 cubic inches.
Consider the attached figure. If AB has length 1, then BC has length sin(15°) and CD (the altitude of triangle ABC) has length sin(15°)·cos(15°).
By the double angle formula for sin(α), ...
... sin(2α) = 2sin(α)cos(α)
Rearranging, this gives
... sin(α)·cos(α) = sin(2α)/2
We have
... CD = sin(15°)·cos(15°) = sin(2·15°)/2
... CD = sin(30°)/2 = (1/2)/2 = 1/4
That is, the altitude, CD, is 1/4 the hypotenuse, AB, of triangle ABC.
