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)=(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)=(adjacent)/(hypotenuse)`

Knowing that:

α = 41°

hypotenuse = 9

Then,

`\begin{gathered} \cos (41)=(x)/(9) \\ \end{gathered}`

Now, solve the equation.

`0.7547=(x)/(9)`

Multiplying both sides by 9:

`\begin{gathered} 0.7547\cdot9=(x)/(9)\cdot9 \\ 6.79=x \end{gathered}`