Question

In the adjoining figure, ∠B=90°, ∠BAC=θ°, BC=CD=4 cm and AD=10 cm.Find cosθ.
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Answer 1

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...

$( Itz ❤Aakanksha❤ here! ) {}^{}$

Answer 2

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...