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Misha Larkins [42]

3 years ago

5

How far apart in feet are Marcus and Joel. Please round your answer to the nearest tenth of a foot

1 answer:

Pavel [41]3 years ago

8 0

Answer:

The distance between Marcus and Joel is approximately 127.3 feet.

Step-by-step explanation:

The distances between Jean to Joel, Jean to Marcus and Marcus to Joel form a right triangle where the distance from Marcus to Joel is the hypothenuse. We can measure the distance from Jean to Marcus and Jean to Joel by using the grid provided, since they're along the same axis. This is shown below:

d(Jean, Marcus) = Jean(x) - Marcus(x) = 100 - 10 = 90 feet

d(Jean, Joel) = Jean(y) - Joel(y) = 90 - 0 = 90 feet

We can apply the pythagora's theorem to find the distance between Marcus and Joel.

d(Marcus,Joel)² = d(Jean,Marcus)² + d(Jean,Joel)²

d(Marcus,Joel)² = (90)² + (90)²

d(Marcus,Joel)² = 2*(90)²

d(Marcus, Joel) = sqrt(2*(90)²) = 90*sqrt(2) = 127.279 feet

The distance between Marcus and Joel is approximately 127.3 feet.

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<img src="https://tex.z-dn.net/?f=%28%20%5Csin%5E%7B2%7D%20%28%20%5Cfrac%7B%5Cpi%7D%7B%204%20%7D%20%20-%20%20%5Calpha%20%29%20%2

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$\sin^2 (\frac{\pi}{4} - \alpha) = \frac{1}{2}(1 - \sin 2\alpha)$

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$\dfrac{1 - \cos [2(\frac{\pi}{4} - \alpha)]}{2} = \frac{1}{2}(1 - \sin 2\alpha)$

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