In the adjoining figure, ∠B = 90°, ∠BAC = θ°, BC = CD = 4 cm an

1.	In the adjoining figure, ∠B = 90°, ∠BAC = θ°, BC = CD = 4 cm and AD=10 cm. Find (i) sinθ and (ii) cosθ.
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 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

In the adjoining figure, ∠B = 90°, ∠BAC = θ°, BC = CD = 4 cm and AD=10 cm. Find (i) sinθ and (ii) cosθ.

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 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