Question

If cos C = 3/5, calculate tan C​

Answer 1

Answer:

tan c 2/5

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Answer 2

Step-by-step explanation:

Lets draw the right angle triangle with the above mentioned details

Given thing are

Tan Θ = 3/5

we know that Tan Θ = Opposite Side/Adjacent Side, so we get

Opposite Side = 3

Adjacent Side = 5

Hypotenuse : BC = ?

Adjacent Side : AB = 5 (Adjacent to ∠ Θ)

Opposite Side : AC = 3 (Opposite to ∠ Θ)

To find the Hypotenuse - BC , we use Pythagoras theorem ((Hypotenuse)2 = (Leg 1)2 + (Leg 2)2)

__________

BC = √ AB2 + AC2

_______

BC = √ 52 + 32

_______

BC = √ 25 + 9

__

BC = √ 34

Now we will try to simplify square root of 34. As no pairs can be made the final value will be

__

BC = √ 34

So Sin, Cos and Tan will be as follows -

Sin Θ = Opposite Side / Hypotenuse

___

Sin Θ = 3 / √ 34

Cos Θ = Adjacent Side / Hypotenuse

___

Cos Θ = 5 / √ 34

Tan Θ = Opposite Side / Adjacent Side

Tan Θ = 3 / 5