Question

Find sin (ABC + 60) NEED QUICK 100 PPOINTS

Answer 1

Answer:

B

Step-by-step explanation:

using the addition identity for sine

sin(A + B) = sinAcosB + cosAsinB

using the sine and cosine ratios in the right triangle

sinABC = $\frac{opposite}{hypotenuse}$ = $\frac{AC}{AB}$ = $\frac{4}{5}$

cosABC = $\frac{adjacent}{hypotenuse}$ = $\frac{BC}{AB}$ = $\frac{3}{5}$

using the exact values

sin60° = $\frac{\sqrt{3} }{2}$ , cos60° = $\frac{1}{2}$

Then

sin(ABC + 60)

= sinABC cos60 + cosABC sin60

= ( $\frac{4}{5}$ × $\frac{1}{2}$ ) + ($\frac{3}{5}$ × $\frac{\sqrt{3} }{2}$ )

= $\frac{4}{10}$ + $\frac{3}{10}$ $\sqrt{3}$

= $\frac{2}{5}$ + $\frac{3}{10}$ $\sqrt{3}$

Answer 2

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