Question

Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth. The diagram is not drawn to scale. (image attached)thank you ! :)

Answer 1

Given:

A right triangle is given. One angle is 45 degrees and the sides of the triangle are as:

Adjacent = 7

Opposite = y

Hypotenuse = x

Required:

Find the missing sides of the triangle.

Explanation:

We know that the sum of all the angles of the triangle is 180 degrees.

Let the missing angle is x.

$\begin{gathered} x+45\degree+90\degree=180\degree \\ x+135\degree=180\degree \\ x=180\degree-135\degree \\ x=45\degree \end{gathered}$

Now to find the missing sides use the folllowing trigonometric ratio.

$\begin{gathered} cos\theta=\frac{adj.}{hyp.} \\ tan\theta=\frac{opp.}{adj.} \end{gathered}$$\begin{gathered} cos45\degree=\frac{7}{x} \\ \frac{1}{\sqrt{2}}=\frac{7}{x} \\ x=7\sqrt{2} \\ x=7(1.414) \\ x=9.899 \\ x=9.9 \end{gathered}$$\begin{gathered} tan45\degree=\frac{y}{7} \\ 1=\frac{y}{7} \\ y=7 \end{gathered}$

Final Answer:

The missing sides of the triangle are as:

x= 9. 9

y = 7