Find the length of BD.

In the adjoining figure, AB = 4 m and ED = 3 m.

If sin α = 3/5 and cos β = 12/13, find the length of BD.

Trigonometric Ratios Class 9 ICSE ML Aggarwal img 45

Answer :

sin α = AB/AC = 3/5

AB = 3 and AC = 5

AC2 = AB2 + BC2

52 = 32 + BC2

25 = 9 + BC2

⇒ BC2 = 25 – 9 = 16

BC2 = 42

⇒ BC = 4

tan α = AB/BC = 4/5

cos β = CD/CE = 12/13

CD = 12 and CE = 13

CE2 = CD2 + ED2

132 = 122 + ED2

ED2 = 132 – 122

⇒ ED2 = 169 – 144 = 25

ED2 = (5)2

⇒ ED = 5

⇒ tan β = ED/CD = 5/12

tan α = AB/BC = 4/BC

¾ = 4/BC

⇒ BC = (4×4)/3 = 16/3 m

tan β = ED/CD = 3/CD

⇒ 5/12 = 3/CD

CD = (12 × 3)/5 = 36/5 m

Here,

BD = BC + CD

= 16/3 + 36/5

Taking LCM

= (80 + 108)/15

= 188/15 m

= 12 8/15 m

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