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ML Aggarwal Solutions Class 9 Mathematics Solutions for Trigonometric Ratios Exercise 17 in Chapter 17 - Trigonometric Ratios
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In triangle ABC, AB = 15 cm, AC = 15 cm and BC = 18 cm.
Answer:
Here ABC is a triangle in which
AB = 15 cm, AC = 15 cm and BC = 18 cm
Draw AD perpendicular to BC, D is mid-point of BC.
Then, BD – DC = 9 cm
in right-angled triangle ABD,
By Pythagoras theorem, we get
\begin{array}{l} A B^{2}=A D^{2}+B D^{2} \\ A D^{2}=A B^{2}-B D^{2} \end{array}
\begin{array}{l} A D^{2}=(15)^{2}-(9)^{2} \\ A D^{2}=225-81 \\ A D^{2}=144 \\ A D-12 \mathrm{cm} \end{array}
(i) cos ∠ABC = Base// Hypotenuse
(In right angled ∆ABD, ∠ABC = ∠ABD)
= BD / AB
= 9/15
= 3/5
(ii) sin ∠ACB = sin ∠ACD
= perpendicular/ Hypotenuse
= AD/AC
= 12/15
= 4/5
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