Question

If angle B=90° BC=CD=a/2,Angle BAC=0° and AD=b Then Find the values of 1)sin theta 2) cos theta
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Answer 1

Answer:

Draw a triangle using given instructions: From figure:

Δ ABC and Δ ABD are right angled triangles where

AD = 10 cm BC = CD = 4 cm BD = BC + CD = 8 cm By Pythagoras theorem:

AD2 = BD2 + AB2 (10)2 = (8)2 + AB2 100 = 64 + AB2 AB2 = 36 = (6)2 or AB = 6 cm Again, AC2 = BC2 + AB2 AC2 = (4)2 + (6)2 AC2 = 16 + 36 = 52 or AC = √52 = 2√13 c

(i) Find sin θ sin θ = BC/AC = 4/2√13 = 2√13/13

(ii) Find cos θ cosθ = AB/AC = 6/2√13 = 3/