Question

triangle I have the hypotenuse which is 9 and a 41 degree angle need to find the leg

Answer 1

To find the legs of a right triangle, you can use the following relations:

$\begin{gathered} \sin (\alpha)=\frac{opposite}{hypotenuse}_{} \\ \cos (\alpha)\frac{\text{adjacent}}{hypotenuse} \\ \tan (\alpha)=\frac{opposite}{\text{adjacent}} \end{gathered}$

In this question, the hypotenuse and a angle of 41° is given.

You need to find x, that is, the adjacent side to 41°.

So, let's use an equation that uses information of the adjacent side and hypotenuse. This equation is:

$\cos (\alpha)=\frac{adjacent}{hypotenuse}$

Knowing that:

α = 41°

hypotenuse = 9

Then,

$\begin{gathered} \cos (41)=\frac{x}{9} \\ \end{gathered}$

Now, solve the equation.

$0.7547=\frac{x}{9}$

Multiplying both sides by 9:

$\begin{gathered} 0.7547\cdot9=\frac{x}{9}\cdot9 \\ 6.79=x \end{gathered}$