Question

Use the information in the figure shown below to find the length of x.3х58

Answer 1

We have two triangles with the same angles, then, they're are proportional to each other.

By the pythagorean theorem we can find the missing side of the smallest triangle:

pythagorean theorem:

`a^2+b^2=c^2`

Where 'c' represents the hypotenuse, and 'a' and 'b' represent the other two sides. Applying this theorem in the smallest triangle we have the following relation:

`3^2+b^2=5^2\text{ }\Rightarrow\text{ b = 4}`

Now that we have our missing side, we can compare the smallest triangle with the biggest triangle.

The ration between 4 and 8 is the same of the hypotenuses of both triangles( x and 5)

Then, we have the following equation:

`(4)/(8)=(5)/(x)\Rightarrow\text{ 4 }*\text{ x = 5 }*\text{ 8}`

Just solving this equation, we get the following result

`\begin{gathered} x\text{ = }(40)/(4)\text{ } \\ x\text{ = 10} \end{gathered}`