Let the base of triangle ABC be " x ".
Now, let's draw a height from side x to angle C .
This makes a right triangle with the hypotenuse of y .
sin 70° = opposite / hypotenuse
sin 70° = height / y
y sin 70° = height
area of triangle ABC = (1/2)(base)(height)
area of triangle ABC = (1/2)(x)(y sin 70°) This equals 30 because the problem says so.
Now let's look at triangle PQR. Let the base be x .
This makes its height = y sin 110°
And the area of PQR = (1/2)(x)(y sin 110°)
Let's say
30 = (1/2)(x)(y sin 70°)
a = (1/2)(x)(y sin 110°) We want to know what a equals.
30 / a = [ (1/2)(x)(y sin 70°) ] / [ (1/2)(x)(y sin 110°) ]
30 / a = sin 70° / sin 110°
30 / a = 1
30 = a