Why angle C?

Geometry Level 3

The length of CD is 7. Calculate the angle BCD to one decimal place in degrees.

This diagram is not drawn to scale.


The answer is 31.7.

Syed Hamza Khalid by Syed Hamza Khalid , 17, France

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1 solution

Consider the diagram on the left.

cos ⁡ 30 = y 5 \cos~30=\dfrac{y}{5} ⟹ \implies y = 5 cos ⁡ 30 y=5\cos~30

tan ⁡ C = y 7 = 5 cos ⁡ 30 7 \tan~C=\dfrac{y}{7}=\dfrac{5\cos~30}{7}

C = t a n − 1 ( 5 cos ⁡ 30 7 ) = C=tan^{-1}\left(\dfrac{5\cos~30}{7}\right)= 31. 7 ∘ \boxed{31.7^\circ}

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How do you get such kind of diagram? Plz tell

Syed Hamza Khalid - 3 years, 8 months ago

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