a box contains 2 triangles, 2 square, 2 rectangle and 2 heart shapes
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How many shapes are in the box in total? There are 8 shapes in total. Show more…
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The rectangular box shown in the figure has dimensions $8^{\prime \prime} \times 6^{\prime \prime} \times 4^{\prime \prime} .$ Approximate the angle $\theta$ formed by a diagonal of the base and a diagonal of the $6^{\prime \prime} \times 4^{\prime \prime}$ side.
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(a) Consider a box whose sides have lengths $a$, $b,$ and $c .$ Use the Theorem of Pythagoras to show that a diagonal of the box has length $d=$ $\sqrt{a^{2}+b^{2}+c^{2}}$ [Hint: Use the Theorem of Pythagoras to find the length of a diagonal of the base and then again to find the length of a diagonal of the entire box.] (b) Use the result of part (a) to derive formula (2).
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