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uysha [10]
2 years ago
7

Suppose each edge of the cube shown in the figure is 10 inches long. Find the sine and cosine of the angle formed by diagonals D

E and DG.

Mathematics
1 answer:
tatiyna2 years ago
4 0

Check the picture below.

sin(EDG )=\cfrac{\stackrel{opposite}{10}}{\underset{hypotenuse}{10\sqrt{3}}}\implies sin(EDG )=\cfrac{1}{\sqrt{3}}\implies sin(EDG )=\cfrac{1}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{sin(EDG )=\cfrac{\sqrt{3}}{\sqrt{3^2}}\implies sin(EDG )=\cfrac{\sqrt{3}}{3}} \\\\[-0.35em] ~\dotfill

cos(EDG )=\cfrac{\stackrel{adjacent}{10\sqrt{2}}}{\underset{hypotenuse}{10\sqrt{3}}}\implies cos(EDG )=\cfrac{\sqrt{2}}{\sqrt{3}}\implies cos(EDG )=\cfrac{\sqrt{2}}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{cos(EDG )=\cfrac{\sqrt{6}}{\sqrt{3^2}}\implies cos(EDG )=\cfrac{\sqrt{6}}{3}}

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Answer:

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Step-by-step explanation:

8. In this problem, 118° is corresponding to ∠1, meaning they are congruent. ∠2 is supplementary with ∠1, meaning that together, they equal 180°. So, to get ∠2, you must subtract 118° from 180°

9. In this problem, 72° is same side interior with ∠1, meaning they are congruent. ∠2 is supplementary with ∠1, so you do 180°-72°=  108°

10. In this problem, ∠1 is vertical angles with 127°, making them equal to each other. ∠2 is corresponding with 127°, making them also equal.

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2 years ago
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Mashutka [201]

Answer:

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Step-by-step explanation:

Given

x = y + 2

Required

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<em>Since they are not of the same form, then the given equation do not show direct variation</em>

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