Convert tan(段) to juchart
Learn how to convert
1
tan(段) to
juchart
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(tan(段)\right)={\color{rgb(20,165,174)} x}\left(juchart\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(square \text{ } meter\right)\)
\(\text{Left side: 1.0 } \left(tan(段)\right) = {\color{rgb(89,182,91)} \dfrac{1.2 \times 10^{5}}{121.0}\left(square \text{ } meter\right)} = {\color{rgb(89,182,91)} \dfrac{1.2 \times 10^{5}}{121.0}\left(m^{2}\right)}\)
\(\text{Right side: 1.0 } \left(juchart\right) = {\color{rgb(125,164,120)} 4.5 \times 10^{3}\left(square \text{ } meter\right)} = {\color{rgb(125,164,120)} 4.5 \times 10^{3}\left(m^{2}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(tan(段)\right)={\color{rgb(20,165,174)} x}\left(juchart\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.2 \times 10^{5}}{121.0}} \times {\color{rgb(89,182,91)} \left(square \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 4.5 \times 10^{3}}} \times {\color{rgb(125,164,120)} \left(square \text{ } meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.2 \times 10^{5}}{121.0}} \cdot {\color{rgb(89,182,91)} \left(m^{2}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 4.5 \times 10^{3}} \cdot {\color{rgb(125,164,120)} \left(m^{2}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.2 \times 10^{5}}{121.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{2}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 4.5 \times 10^{3}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{2}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1.2 \times 10^{5}}{121.0} = {\color{rgb(20,165,174)} x} \times 4.5 \times 10^{3}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{1.2 \times {\color{rgb(255,204,153)} \cancelto{10^{2}}{10^{5}}}}{121.0} = {\color{rgb(20,165,174)} x} \times 4.5 \times {\color{rgb(255,204,153)} \cancel{10^{3}}}\)
\(\text{Simplify}\)
\(\dfrac{1.2 \times 10^{2}}{121.0} = {\color{rgb(20,165,174)} x} \times 4.5\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 4.5 = \dfrac{1.2 \times 10^{2}}{121.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{4.5}\right)\)
\({\color{rgb(20,165,174)} x} \times 4.5 \times \dfrac{1.0}{4.5} = \dfrac{1.2 \times 10^{2}}{121.0} \times \dfrac{1.0}{4.5}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{4.5}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{4.5}}} = \dfrac{1.2 \times 10^{2} \times 1.0}{121.0 \times 4.5}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.2 \times 10^{2}}{121.0 \times 4.5}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.2203856749\approx2.2039 \times 10^{-1}\)
\(\text{Conversion Equation}\)
\(1.0\left(tan(段)\right)\approx{\color{rgb(20,165,174)} 2.2039 \times 10^{-1}}\left(juchart\right)\)
