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trig problem

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In right triangle ABC, shown below, cos B = $$7/10$$. What is tan C?

May 1, 2022

#1
+214
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AB is the adjacent for B, and BC is the hypotenuse. Since AB/BC = AB/10 = 7/10, AB=7.

Using the Pythagorean theorem, you can deduce that AC = $$\sqrt {51}$$

For C, AB is the opposite and AC is the adjacent, so tan C would be $$7\sqrt{51}\over51$$.

My trigonometry skills are... lacking, so I would read this over to see if I made any fundamental mistakes.

May 1, 2022
#2
+1351
+3

We know that $$\cos = {\text{adjacent} \over \text{hypotenuse}}$$

This means that $$AB = 7$$

Applying the Pythagorean Theorem, we know that $$AC = \sqrt{51}$$.

We also know that $$\tan = {\text{opposite} \over \text{adjacent}}$$

Thus, $$\tan{C} = {7 \over \sqrt{51}} = \color{brown}\boxed{7 \sqrt{51} \over 51}$$, just as whyamidoingthis found :)

May 1, 2022
edited by BuilderBoi  May 1, 2022