Question

Find sin (ABC + 60) NEED QUICK 100 PPOINTS

Answer 1

sin<ABc

• Perpendicular/Hypotenuse
• 4/5

cos<ABC

• Base/Hypotenuse
• 3/5

Now

• sin(<ABC+60)
• sin<ABC ×cos60+cos<ABC×sin60
• 4/5(1/2)+3/5(√3/2)
• 2/5+3/10√3

Answer 2

B

Explanation:

using the addition identity for sine

sin(A + B) = sinAcosB + cosAsinB

using the sine and cosine ratios in the right triangle

sinABC =
`(opposite)/(hypotenuse)` =
`(AC)/(AB)` =
`(4)/(5)`

cosABC =
`(adjacent)/(hypotenuse)` =
`(BC)/(AB)` =
`(3)/(5)`

using the exact values

sin60° =
`(√(3) )/(2)` , cos60° =
`(1)/(2)`

Then

sin(ABC + 60)

= sinABC cos60 + cosABC sin60

= (
`(4)/(5)` ×
`(1)/(2)` ) + (
`(3)/(5)` ×
`(√(3) )/(2)` )

=
`(4)/(10)` +
`(3)/(10)`
`√(3)`

=
`(2)/(5)` +
`(3)/(10)`
`√(3)`