Sine, cosine and tangent of an angle represent the ratios that are always true for given angles. Remember these ratios only apply to right triangles.

The 3 triangles pictured on the left illustrate this.

Although the side lengths of the right triangles are different, each one has a 37° angle, and as you can see, the sine of 37 is always the same!
In other words, sin(37) is always .6 !

Problem 6)
What is the tangent ratio of $$\angle BAC$$ in the triangle on the right?

Answer

Remember that the tangent ratio is the side opposite /adjacent sides.
Therefore
$$
tan(BAC) = \frac{opposite}{adjacent} = \frac{24}{7} = 3.4285714285714284
$$

problem 11) Which angle on the left has a tangent of $$\frac{3}{4}$$ ?

Answer

$$
tangent = \frac{opposite}{adjacent}
$$
So which angle has a tangent that is equivalent to $$\frac{3}{4}$$ ?
$$ \angle L $$
$$ tan(L) = \frac{9}{12} $$

Load More Problems Like This

problem 12 Which angle on the left has a cosine of $$\frac{3}{5}$$ ?

Answer

$$
cosine = \frac{adjacent}{hypotenuse}
$$
So which angle has a cosine that is equivalent to $$\frac{3}{5}$$ ?
$$ \angle K $$
$$ cos(k) = \frac{9}{15} $$

problem 13 Which angle on the left has a tangent $$\approx$$ .29167?

Answer

This is a little trickier because you are given the ratio as a decimal; however, you only have two options. Either $$ \angle A $$ or $$\angle C $$

$$
tan( \angle A) = \frac{48}{14} \approx 3.42857
\\
\color{Red}{
tan( \angle C) = \frac{14}{48} \approx.29167
}
$$

problem 14 Which angle on the left has a tangent of 2.4?

Answer

Again, there are two options (angles R or P), but since your ratio is greater than 1 you might quickly be able to notice that it must be R

In the triangle on the left, which angle has a sine ratio of 2.6?

Answer

There is no angle that has a sine of 2.6 .

Remember that the maximum value of the sine ratio is 1 .

The same, is true, by the way of cosine ratio (max value is 1)

Word Problems

problem 15) In $$\triangle JKL$$, sin(k) = $$\frac{3}{5} $$, what is tan(k)?

Step 1

It's easiest to do a word problem like this one, by first drawing the triangle and labelling the sides. We know the opposite side of $$ \angle K$$ and we know the hypotenuse

To get the tangent ratio we need to know the length of the adjacent side