How to find the tangent of an angle

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ACT Math › How to find the tangent of an angle

Questions 1 - 4
1

If the sine of an angle equals , and the cosine of the same angle equals , what is the tangent of the angle?

Explanation

The cosine of the angle is and since that is a reduced fraction, we know the hypotenuse is and the adjacent side equals .

The sine of the angle equals , and since the hyptenuse is already we know that we must multiply the numerator and denominator by to get the common denominator of . Therefore, the opposite side equals .

Since , the answer is .

2

Triangle

What is the tangent of C in the given right triangle??

Explanation

Tangent = Opposite / Adjacent

3

Triangle

Triangle ABC shown is a right triangle. If the tangent of angle C is , what is the length of segment BC?

Explanation

Use the definition of the tangent and plug in the values given:

tangent C = Opposite / Adjacent = AB / BC = 3 / 7

Therefore, BC = 7.

4

Consider a right triangle with an inner angle .

If

and

what is ?

Explanation

The tangent of an angle x is defined as

Substituting the given values for cos x and sin x, we get

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