In the adjoining figure, ∠B=90°, ∠BAC=θ°, BC=CD=4 cm and AD=10 cm.Find cosθ.
Answers
Hey mate,
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 cm
(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/√13 = 3√13/13
Hope it helps...
Hey mate,
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 cm
(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/√13 = 3√13/13