An engineer is required to survey a nonrectangluar plot of land but is unable to measure side UT directly. The followng data are taken; RU=130 meters, RS=12m ST=90m, angle RST=115, and angle RUT=100.

Question

Calculate the length of side UT and the area of the plot.

The picture is a nonrectangular with four sides however with different angles and length. But lengths are straight ,no curves. so basically, it is a rectangle shape with different lengths and slanted lengths.

I drew the picture and I separated the shape into two triangles.

The letters I used to name the side in order are SRUT.

I used law of cosines to determine an unknown length RT for which I got 132m.

RT is the line in the middle I used to get two triangles.

Then I used law of sine to get the only angle R. I got 38 degrees. And I used the 180 rule to figure out another angle. I got 27 degrees

My question is if you can check my answers, because they sound wrong and also to guide me on how to finish this question.

Answer 1

RT^2 = 12^2+90^2 - 2 (12)(90)(cos115)
RT ^2 = 144 + 8100- 2106(-.423)
RT^2 = 8244+890 = 9134
so
RT = 95.6 I DO NOT GET 132 !