Question

State the formulas for the area of a triangle ABC that were derived using the law of sines.

Answer 1

Given

a triangle ABC

Find

Area of a triangle using the laws of sines

Step-by-step explanation

As area of triangle =

`(1)/(2)* base* height`

since, it is a right angle triangle.

Assume the sine of angle A

`sinA=\frac{opposite\text{ side}}{hypotenuse}`

so, we have

`sinA=(h)/(c)`

hence,

`h=csinA`

now, put the value of h in area of triangle,

`Area\text{ of triangle =}(1)/(2)* b* csinA=(1)/(2)bcsinA`

similarly we can write for the sinB and SinC

`(1)/(2)absinC\text{ and }(1)/(2)acsinB`

Final Answer

Area of triangle in the law of sines is

`(1)/(2)bcsinA`