What is the value of sqrt(80^2+650^2-2(80)(650)cos(135)) ?

The value of sqrt(80^2+650^2-2(80)(650)cos(135)) is sqrt(80^2+650^2-2*80*650(-(\sqrt{2))/2)}

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sqrt(80^2+650^2-2(80)(650)cos(135))

8 0^{2} + 65 0^{2} - 2 (80) (650) cos (13 5^{\circ})

8 0^{2} + 65 0^{2} - 2 \cdot 80 \cdot 650 (- \frac{2}{2})

Solution steps

8 0^{2} + 65 0^{2} - 2 (80) (650) cos (13 5^{\circ})

= 8 0^{2} + 65 0^{2} - 2 \cdot 80 \cdot 650 cos (13 5^{\circ})

Use the following trivial identity:

cos (13 5^{\circ}) = - \frac{2}{2}

= 8 0^{2} + 65 0^{2} - 2 \cdot 80 \cdot 650 (- \frac{2}{2})

1 - 2 sin^{2} (3 2^{\circ})

arctan (1 \frac{1}{3})

sec (arcsin (\frac{8}{17}))

tan (\frac{29 π}{4})

52 (tan (3 9^{\circ}))

What is the value of sqrt(80^2+650^2-2(80)(650)cos(135)) ?
The value of sqrt(80^2+650^2-2(80)(650)cos(135)) is sqrt(80^2+650^2-2*80*650(-(\sqrt{2))/2)}