SOLUTION: In triangle ABC, side AB = x, angle B = 70 degrees, and side BC = y. In triangle PQR, side PQ = x, angle Q = 110 degrees, and side QR = y. The area of ABC is 30. What is the a

Question 973150: In triangle ABC, side AB = x, angle B = 70 degrees, and side BC = y.
In triangle PQR, side PQ = x, angle Q = 110 degrees, and side QR = y.
The area of ABC is 30. What is the area of PQR?
The answer is given as 30.
I can see that the two angles are opposites of each other, but as these aren't right triangles, or similar triangles, how do you prove that the areas are the same. What theorem is this based on?
Thank you.
Helen
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Area = b*h/2
h = side x or y times cos of the angle
cos(70) = cos(110)
--> same h, same area.
RELATED QUESTIONS
In a triangle ABC, the angle at A is 57 degrees, the angle at B is 28 degrees, and the... (answered by Fombitz)

In a triangle ABC, the angle at B is 155 degrees, the length of side BC is 29, and the... (answered by Cromlix)

In triangle ABC , angle B = 76 degrees , side a=45cm and side b=53cm . Find angle... (answered by 10301650,Alan3354)

In triangle ABC, side AB is x longer than side BC . The ray bisecting angle B intersects... (answered by robertb)

Point X is on side Line AC of Triangle ABC such that angle AXB =angle ABX, and angle ABC... (answered by simranb)

In (triangle)PQR, m <(angle)Q=90 degrees, PQ=1, and QR=3. The value for sec <(angle)R is... (answered by Alan3354)

ABC is an isosceles triangle with side AB= side AC. Line BC is produced to D such that... (answered by mananth,math_tutor2020)

Draw a right angled triangle ABC with vertical side AB, horizontal side BC and (answered by psbhowmick)