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From the given figure, prove that θ + ϕ = 90°. Also prove that there are two other right angled triangles. Find sin α, cos β and tan ϕ.

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From (1), (2), (3) 

(∴ By Pythagoras theorem, in a right angled triangle square of hypotenuse is equal to sum of the squares of other two side)

And also in the figure, ∆ADC, ∆DBC are two other triangles. 

As per the data given, 

92 + 122 = 81 + 144 = 225 = 152

∴ ∆ ADC is a right angled triangle, then 122 + 162 

= 144 + 256 = 400 = 202 

∴ ∆ DBC is also a right angled triangle

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