Find the height $ h $ of a rhombus if area $A = 480$ and diagonal $d_2 = 48$.

Problem has no solutions.

STEP 1: find diagonal $ d1 $

To find diagonal $ d1 $ use formula:

$$ A = \dfrac{ d_1 \cdot d_2 }{ 2 } $$

After substituting $ A = 480 $ and $ d_2 = 48 $ we have:

$$ 480 = \dfrac{ d_1 \cdot 48 }{ 2 } $$$$ 480 \cdot 2 = d_1 \cdot 48 $$$$ 960 = 48 \cdot d_1 $$$$ d_1 = \dfrac{ 960}{ 48 } $$$$ d_1 = 20 $$

STEP 2: find angle $ \alpha $

To find angle $ \alpha $ use formula:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ d_2 }{ d_1 } $$

After substituting $ d_2 = 48 $ and $ d_1 = 20 $ we have:

$$ \sin \left( \frac{ \alpha }{ 2 } \right) = \dfrac{ 48 }{ 20 } $$ $$ \sin \left( \frac{ \alpha }{ 2 } \right) = \frac{ 12 }{ 5 } $$ $$ \frac{ \alpha }{ 2 } = \arcsin\left( \frac{ 12 }{ 5 } \right) $$

$ \arcsin(2.4) $ is not defined $ \Longrightarrow $ The problem has no solution.

Rhombus Calculator