Consider A(3,60),B(8,150) and O(0,0). Find the area of triangle AOB?
The easiest way to start solving a question like that is to make a plot of the points. It need not be extremely accurate but it will give you an idea of what you have to do. After plotting the points you will see that it is easy to calculate the lengths OA and OB by simply using the Pythagorean Theorem. OA=sqrt(3^2 + 60^2)= 60.07 units approximately and OB= sqrt(8^2 + 150^2)= 150.21 units approximately. The next thing you have to do is find the angle AOB. You do this by finding the angles that the lines OA and OB make with the x axis and then subtracting the big angle from the small one. Let’s name the angle that OA makes with the x axis θ and the angle OB makes with the x axis φ. tan(θ)=60/3 and tan(φ)=150/8. Use a calculator to find the two angles and you should find θ=87.1deg and φ=86.9deg. Now find the angle AOB which is simply θ-φ=0.2deg (approximately). We now use the formula for the area of the triangle: A=(OA*OB*sin(AOB))/2 and you find an area of 14.96 or approximately 15 square units.
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