Question

How would I do b I’m confused it’s asking for each 45-45-90 triangle find a and b

Answer 1

In every 45-45-90 triangle, both legs have the same length and the hypotenuse has the length of a leg multiplied by √2.

The hypotenuse is the side opposite to the right angle (90º). The other two sides are the legs that have the same length.

In the question b., the hypotenuse has a length b and the missing leg has a length a.

Since the leg of the triangle has a measure of 2.5ft, then the leg a must have the same measure. Then:

`a=2.5ft`

The hypotenuse has the length of a leg multiplied by √2. Then:

`\begin{gathered} b=2.5*\sqrt[]{2}ft \\ =\frac{2*2.5*\sqrt[]{2}}{2}ft \\ =\frac{5\cdot\sqrt[]{2}}{2}ft \\ \approx3.5355\ldots ft \end{gathered}`

Therefore, the lengths of a and b in the question b., are:

`\begin{gathered} a=2.5ft \\ b=\frac{5\cdot\sqrt[]{2}}{2}ft\approx3.5ft \end{gathered}`