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

 

 May 1, 2022
 #1
avatar+214 
+2

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
avatar+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

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