Question

Answer ASAP Find tanθ, where θ is the angle shown. Give an exact value, not a decimal approximation.

Answer 1

Answer:  24/7

This is the same as writing the fraction $\frac{24}{7}$

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Explanation:

Use the pythagorean theorem to find the missing side.

$a^2 + b^2 = c^2\\\\a^2 + 24^2 = 25^2\\\\a^2 + 576 = 625\\\\a^2 = 625 - 576\\\\a^2 = 49\\\\a = \sqrt{49}\\\\a = 7$

The horizontal side of the right triangle is 7 units long.

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The $\tan(\theta)$ is the ratio of the opposite over adjacent.

$\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(\theta) = \frac{\text{vertical}}{\text{horizontal}}\\\\\tan(\theta) = \frac{24}{7}$