Question

If a and b are the measures of two first quadrant angles and sin a = 4/9 and sin b = 2/5 find sin(a+b).

Answer 1

C

Explanation:

Edge2021

Answer 2

`sin(a+b)=(4√(21)+2√(65))/(45)`

Explanation:

we are given

`sin(a)=(4)/(9)`

`sin(b)=(2)/(5)`

Firstly, we will draw triangle

we get

`cos(a)=(√(65) )/(9)`

`cos(b)=(√(21) )/(5)`

now, we can sue formula

`sin(a+b)=sin(a)cos(b)+cos(a)sin(b)`

now, we can plug values

`sin(a+b)=(4)/(9)* (√(21) )/(5)+(√(65) )/(9)* (2)/(5)`

now, we can simplify it

`sin(a+b)=(4√(21)+2√(65))/(45)`