QuestionSolve for the long leg and for the hypotenuse of the $30-60-90$ thangle. a. $a=20$ and $b=10$ b. $a=20$ and $b=10 \sqrt{3}$ c. $a=10$ and $b=10 \sqrt{3}$ d. $a=10 \sqrt{3}$ and $b=20$

Studdy Solution
In part (d), if $a = 10\sqrt{3}$ is the long leg, then the short leg should be $10$ and the hypotenuse should be $20$. Since $b = 20$, this matches the expected ratio. Therefore, the short leg is $10$, the long leg is $10\sqrt{3}$, and the hypotenuse is $20$.
The solutions for each part are: a. Short leg: $10$, Long leg: $10\sqrt{3}$, Hypotenuse: $20$ b. Short leg: $10$, Long leg: $10\sqrt{3}$, Hypotenuse: $20$ c. Short leg: $10$, Long leg: $10\sqrt{3}$, Hypotenuse: $20$ d. Short leg: $10$, Long leg: $10\sqrt{3}$, Hypotenuse: $20$