Answer:
a = 400/21, b = 580/21
Step-by-step explanation:
Small triangles are similar. Therefore, the sides are proportional
[tex]\dfrac{a}{20}=\dfrac{20}{21}[/tex] cross multiply
[tex]21a=(20)(20)[/tex] divide both sides by 21
[tex]a=\dfrac{400}{21}[/tex]
For b, we can use the Pythagorean theorem:
[tex]b^2=\left(\dfrac{400}{21}\right)^2+20^2\\\\b^2=\dfrac{160000}{441}+400\\\\b^2=\dfrac{160000}{441}+\dfrac{176400}{441}\\\\b^2=\dfrac{336400}{441}\to b=\sqrt{\dfrac{336400}{441}}\\\\b=\dfrac{\sqrt{336400}}{\sqrt{441}}\\\\b=\dfrac{580}{21}[/tex]
