Question

in in triangle abc , €B=90. if A=30, find a is value of of sin a cos b + cos a sin b .
answer please ​

Answer 1

answer is root 3 upon 2

hipe it helps you

Answer 2

Answer:

The value of of sin a cos b + cos a sin b is $\frac{ \sqrt{3} }{2}$

Step-by-step explanation:

Given angle B is 90° and angle A is 30°.

Now we want to find value of $\sin(a) \cos(b) + \cos(a) \sin(b)$

We are putting a=90° and b=30°,

So,$\sin(a) \cos(b) + \cos(a) \sin(b) = sin {90}^{o} \cos( {30}^{o} ) + \cos( {90}^{o} ) \sin( {30}^{o} )$

We know,

$\sin( {90}^{o} ) = 1 \\ \cos( {90}^{o} ) = 0 \\ \sin( {30}^{o} ) = \frac{1}{2} \\ \cos( {30}^{o} ) = \frac{ \sqrt{3} }{2}$

So,$sin {90}^{o} \cos( {30}^{o} ) + \cos( {90}^{o} ) \sin( {30}^{o} ) = 1 \times \frac{ \sqrt{3} }{2} + 0 \times \frac{1}{2} = \frac{ \sqrt{3} }{2} + 0 = \frac{ \sqrt{3} }{2}$

Therefore value of sin a cos b + cos a sin b is $\frac{ \sqrt{3} }{2}$

Another method,

We know,$sin a \: cos b + cos a \: sin b = sin(a+b)$

Here a=90° and b=30°.

So,Sin(a+b)=Sin(90°+30°)=Sin120°=$\frac{ \sqrt{3} }{2}$