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

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

Explanation

$Sine = \frac{opposite}{hypotenuse}. ;Cosine = \frac{adjacent}{hypotenuse}. ;Tangent = \frac{opposite}{adjacent}$

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 $tangent = \frac{opposite}{adjacent},$ , the answer is .

Triangle

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

$\frac{AB}{BC}$

$\frac{AB}{AC}$

$\frac{CB}{AB}$

$\frac{CB}{AC}$

$\frac{AC}{BC}$

Explanation

Tangent = Opposite / Adjacent

Triangle

Triangle ABC shown is a right triangle. If the tangent of angle C is $\frac{3}{7}$ , what is the length of segment BC?

$\sqrt{58}$

$\sqrt{21}$

Explanation

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

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

Therefore, BC = 7.

Consider a right triangle with an inner angle $\left ( x<90^{\circ} \right )$ .

$\cos x=\frac{3}{5}$

and

$\sin x=\frac{4}{5}$

what is $\tan x$ ?

$\frac{4}{3}$

$\frac{3}{4}$

$\frac{1}{5}$

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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