Question

Find the exact value of sin A in simplest radical form.
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Answer 1

Using the law of sines, we have

$\dfrac{AB}{\sin(C)}=\dfrac{BC}{\sin(A)}$

And we know that

$AB=\sqrt{85},\quad BC=6,\quad A=90$

So, the equation becomes

$\sin(A)=\dfrac{BC\sin(C)}{AB}=\dfrac{6\sin(90)}{\sqrt{85}}=\dfrac{6}{\sqrt{85}}$

Answer 2

The value of the sin A in simplest radical form is 0.651 units.

Given-

The triangle given in the image is Right angle triangle.

The value of side AB is $\sqrt{85}$.

The value of side BC is 6.

The value of side CA is 7.

The value of angle ABC is 90 degree (right angle triangle).

Sine law-The law of sine can be used to calculate the remaining sides or angle of the triangle when 2 or more sides or angle are known. Using sine law-

$\dfrac{AB}{Sin C} =\dfrac{BC}{Sin A}$

Put the values,

$\dfrac{\sqrt{85} }{Sin 90} =\dfrac{6}{Sin A}$

Solve for sinA,

${Sin A}=\dfrac{6\times Sin (90)}{\sqrt{85} }$

$Sin A=\dfrac{6}{\sqrt{85} }$

$Sin A=0.651$

Hence, the value of the sin A in simplest radical form is 0.651 units.

For more about the right angle triangle follow the link below-

https://brainly.com/question/3770177