A scalaene triangle has 3 sides: RS = 12.1, ST = 19.8, RT = 17.4. NOw i have to find the area of the triangle.
It didn't say which side was the base, so I made side ST the base. Then, I made a dotted line for the height, H. So now there's 2 triangles: RSY, and RYT. Triangle RSY has RS which is 12.1, and angle Y, which is 90 degrees. How can I figure out other information for triangle RSY with only that info? I thought i'd use trigonometric ratios. So, the sin of Y = o/h = i'm not sure. the hypotenous is 12.1, but what is the opposite side for angle Y, which is a right angle?
Sorry, I know this post must seem rambling.... but thats what progress I've made on the qu., lol. I would appreciate any help you may have. I know, I'm not asking for the answer. I just need some step-by-step instructions to guide me though. thank you.
A scalaene triangle has sides:
Find the area of the triangle.
Someone will mention Heron's Formula . . . which is the fastest method.
But, assuming you know Trigonometry, I'll show you another way . . .
We have: . with angles
. . and their respective opposite sides:
The area of the triangle is: .
. . (One-half the product of two sides times the sine of the included angle.)
To find , we use a variation of the Law of Cosines: .
We have: .
. . Then: .
. . Therefore: .
Thanks Soroban! When finding cosT, can I use the cosine law (instead of the variation, cuz i think that's what is expected of me)? i did, and I got
cosT = 25.4167.
cos 25.4167 = 0.9032
so angle T = 25 degrees... which is very different from your answer. i'm not sure why i'm getting a different answer?