Angle

Geometry Level 3

In ABC \color{#D61F06}\text{ABC} triangle

a:b:c=3:7:5 \color{#D61F06}\text{a:b:c=3:7:5}

so what is ∠ B = ? \color{#D61F06}\angle B = ?

6 0 ∘ 60^\circ 9 0 ∘ 90^\circ 3 0 ∘ 30^\circ 12 0 ∘ 120^\circ

Nazmus Sakib by Nazmus sakib , 24, Bangladesh

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1 solution

Nazmus Sakib
Sep 18, 2017

a=3k b=7k c=5k

cos ⁡ B \cos B = a 2 + c 2 − b 2 2 a c \dfrac{a^2+c^2-b^2}{2ac}

= 34 − 49 30 \dfrac{34-49}{30}

= − 15 30 \dfrac{-15}{30}

= − 1 2 \dfrac{-1}{2}

cos ⁡ B = cos ⁡ 12 0 ∘ \cos B = \cos120^\circ

so, ∠ B = 12 0 ∘ \huge\color{#D61F06}\angle B = 120^\circ

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