Use the adjoining figure and find the values of :
1) sin x
2) cos y
3) 3 tan x - 2 sin y + 4 cos y
Answers
Answer:
option 3 is your answer..........
Answer:-
Given: AC = 17 cm , BD = 6 cm , BC = 8 cm
by using phythagoras theoram, P² + B² = H²
BC²+ BD²= CD²
8²+ 6² = CD²
64 + 36 = CD²
100 = CD²
Taking root on both sides , we get
CD = 10 cm
similarly,
AC² = BC² + AB² (:.AB = AD + DC)
17² = 8² + (AD + 6)²
289 = 64 + (AD+6)²
225 = (AD+6)²
Again taking square root on both sides,
15 = AD + 6
AD = 9 cm
hence , AB = 9 + 6 = 15 cm
As we know,
sin x = perpendiular / hypotenuse
cos x = base / hypotenuse
tan x = sin x / cos x
by using above properties ,
In Δ ABC,
cos x = B / H = AB / AC
= 15 / 17
sin x = P / H = BC / AB
= 8 / 15
tan x = sin x / cos x
= (8 / 15) / (15 / 17)
tan x = 8 / 15
In Δ CBD ,
cos y = B / H = BD / CD
= 6 / 10 = 3 / 5
sin y = P / H = BC / CD
= 8/10 = 4/5
(1) sin x = 8/15
(2) cos y = 3/5
(3) 3 tan x - 2 sin y + 4 cos y
⇒ 3×(8/15) -2×(4/5) + 4× (3/5)
⇒ 8/5 -8/5 +12/5
⇒ 12/5
I hope you wil be satisfied by this answer
Thankyou.