Question

What is tan 45°?
A. √3
OB. 1
C.
-~
D. √
OD.
E. 1
2

Answer 1

Answer: B) 1

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Reason:

Draw out a 45-45-90 triangle. This triangle is isosceles with the two legs being the same length. Let's say each is x units long.

The value of tan(45) is equal to the ratio of those leg lengths.

tan(angle) = opposite/adjacent

tan(45) = x/x

tan(45) = 1

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Alternative Method:

Use the unit circle shown below to see that

`\cos(45^(\circ)) = (√(2))/(2)\\\\\sin(45^(\circ)) = (√(2))/(2)\\\\`

Both are equal to the same value, which means dividing them gets us 1

`\tan(45^(\circ)) = (\sin(45^(\circ)))/(\cos(45^(\circ))) = 1`