Question
Find the leg $ b $ of a right triangle if hypotenuse $c = 2 \sqrt{ 17 }\, \text{cm}$ and angle $\alpha = 30^o$.
Answer
$\sqrt{ 51 }\, \text{cm}$
Explanation
To find leg $ b $ use formula:
$$ \cos \left( \alpha \right) = \dfrac{ b }{ c } $$After substituting $\alpha = 30^o$ and $c = 2 \sqrt{ 17 }\, \text{cm}$ we have:
$$ \cos( 30^o ) = \dfrac{ b }{ 2 \sqrt{ 17 } } $$ $$ \frac{\sqrt{ 3 }}{ 2 } = \dfrac{ b }{ 2 \sqrt{ 17 } } $$$$ b = \frac{\sqrt{ 3 }}{ 2 } \cdot 2 \sqrt{ 17 } $$$$ b = \sqrt{ 51 } $$This page was created using
Right Triangle Calculator