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Question
In the given figure, AD is perpendicular to BC. Find: 5 cos x - 12 sin y + tan x
Solution
ΔADB is a right-angled triangle.
∴ AB2
= AB2 + BD2
= 122 + 162
= 144 + 256
= 400
⇒ AB = 20cm
ΔADC is a right-angled triangle.
∴ AC2
= AD2 + DC2
= 122 + 92
= 144 + 81
= 225
⇒ AC = 15cm
5 cos x - 12 sin y + tan x
= `4 - 12 xx "CD"/"AC" + "AD"/"BD"`
= `4 - 12 xx (9)/(15) + (12)/(16)`
= `4 - (36)/(5) + (3)/(4)`
= `(80 - 144 + 15)/(20)`
= `(-49)/(20)`.
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