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प्रश्न
From the given figure, prove that θ + ∅ = 90°. Also prove that there are two other right angled triangles. Find sin α, cos β and tan ∅
उत्तर
In the ΔABC,
AB = 9 + 16 = 25
AC = 15, BC = 20
AB2 = 252
= 625 ...(1)
AC2 + BC2 = 152 + 202
= 225 + 400
= 625 ...(2)
From (1) and (2) we get
AB2 = AC2 + BC2
ABC is a right angle triangle at C ...(Pythagoras theorem)
∴ ∠C = 90°
θ + ∅ = 90°
Also ADC is a right angle triangle ∠ADC = 90° ...(Given)
BDC is also a right angle triangle ∠BDC = 90° ...(since ADB is a straight line sum of the two angle is 180°)
From the given diagram
sin α = `"DC"/"AC" = 12/15 = 4/5`
cos β = `"BD"/"BC" = 16/20 = 4/5`
tan Φ = `"BD"/"CD" = 16/12 = 4/3`
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