Question

In the given figure, AD is perpendicular to BC. Find: 5 cos x - 12 sin y + tan x

Answer 1

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)`.