Question

A Fill in the blank. If necessary, use the slash mark (/) for a fraction bar. If cosg = then tang =

Answer 1

Step-by-step explanation

We can use a right triangle and the below trigonometric ratios.

`\begin{gathered} \cos(\theta)=\frac{\text{ Adjacent leg}}{\text{ Hypotenuse}} \\ \tan(\theta)=\frac{\text{ Opposite leg}}{\text{ Adjacent leg}} \end{gathered}`

In this case, we have:

`\cos(\theta)=(3)/(5)=\frac{\text{Adjacent leg}}{\text{Hypotenuse}}`

As we can see, we need to know the value of the opposite leg. Since it is a right triangle, we can use the Pythagorean theorem formula.

`\begin{gathered} a^2+b^2=c^2 \\ \text{ Where} \\ a\text{ and }b\text{ are the legs} \\ c\text{ is the hypotenuse} \end{gathered}`

Then, we have:

`\begin{gathered} a=3 \\ b=? \\ c=5 \\ a^(2)+b^(2)=c^(2) \\ 3^2+b^2=5^2 \\ 9+b^2=25 \\ \text{ Subtract 9 from both sides} \\ 9+b^2-9=25-9 \\ b^2=16 \\ $$\text{ Apply square root to both sides of the equation}$$ \\ √(b^2)=√(16) \\ b=4 \end{gathered}`

Finally, we have:

Then, we can find the value of tan(θ):

`\begin{gathered} \tan(\theta)=\frac{\text{Opposite leg}}{\text{Adjacentleg}} \\ \tan(\theta)=(4)/(3) \end{gathered}`Answer
`\tan(\theta)=(4)/(3)`