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})

Decimal Notation

708.82939 \dots

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}

cos (13 5^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - \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)}