Question

Solve for the missing side lengths.V1045°A. Ou = 10/2, vV =10./33B. Ou-20v2, v =1033c. Ou = 20v2, v =10D. Ou = 10v2, v = 10

Answer 1

We have a right triangle, where we know that one of the angles (besides the right angle) has a measure of 45°.

Then, the other angle measure can be calculated as:

`\begin{gathered} \alpha+45+90=180 \\ \alpha=180-90-45 \\ \alpha=45\degree \end{gathered}`

Then, as the other angle measure is equal, we have an isosceles triangle.

Then, length v has to be equal to the side with length 10.

With the value of v we can calculate u with the Pythagorean theorem:

`\begin{gathered} u^2=v^2+10^2 \\ u^2=10^2+10^2 \\ u^2=2\cdot10^2 \\ u=\sqrt[]{2}\cdot10 \\ u=10\sqrt[]{2} \end{gathered}`

Answer: u = 10√2, v = 10