What is the value of (2.7*10^{-4})(9.8)tan(36) ?

The value of (2.7*10^{-4})(9.8)tan(36) is (1323sqrt(2)(sqrt(5)-1)sqrt(5-\sqrt{5)})/(2000000)

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(2.7*10^{-4})(9.8)tan(36)

(2.7 \cdot 1 0^{- 4}) (9.8) tan (3 6^{\circ})

\frac{1323 2 ( 5 - 1 ) 5 - 5}{2000000}

Solution steps

(2.7 \cdot 1 0^{- 4}) (9.8) tan (3 6^{\circ})

= \frac{27}{10} \cdot 1 0^{- 4} \cdot \frac{49}{5} tan (3 6^{\circ})

Rewrite using trig identities:

tan (3 6^{\circ}) = \frac{2 ( 5 - 1 ) 5 - 5}{4}

= \frac{27}{10} \cdot 1 0^{- 4} \cdot \frac{49}{5} \cdot \frac{2 ( 5 - 1 ) 5 - 5}{4}

Simplify

\frac{27}{10} \cdot 1 0^{- 4} \cdot \frac{49}{5} \cdot \frac{2 ( 5 - 1 ) 5 - 5}{4} : \frac{1323 2 ( 5 - 1 ) 5 - 5}{2000000}

= \frac{1323 2 ( 5 - 1 ) 5 - 5}{2000000}

sin^{2} (4 5^{\circ}) - cos^{2} (4 5^{\circ})

- sin (30 0^{\circ})

10 \cdot cos (5 2^{\circ})

arctan (22)

arctan (23)

What is the value of (2.7*10^{-4})(9.8)tan(36) ?
The value of (2.7*10^{-4})(9.8)tan(36) is (1323sqrt(2)(sqrt(5)-1)sqrt(5-\sqrt{5)})/(2000000)