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

Answer:

$sin(a+b)=\frac{4\sqrt{21}+2\sqrt{65}}{45}$

Step-by-step explanation:

we are given

$sin(a)=\frac{4}{9}$

$sin(b)=\frac{2}{5}$

Firstly, we will draw triangle

we get

$cos(a)=\frac{\sqrt{65} }{9}$

$cos(b)=\frac{\sqrt{21} }{5}$

now, we can sue formula

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

now, we can plug values

$sin(a+b)=\frac{4}{9}\times \frac{\sqrt{21} }{5}+\frac{\sqrt{65} }{9}\times \frac{2}{5}$

now, we can simplify it

$sin(a+b)=\frac{4\sqrt{21}+2\sqrt{65}}{45}$