SOLUTION: I have a base length of 23.73m. A long side of 16.38m and a short side of 16.33m. May you help me find the perpendicular height of this scalene triangle. I have no angles provided.

Algebra ->  Triangles -> SOLUTION: I have a base length of 23.73m. A long side of 16.38m and a short side of 16.33m. May you help me find the perpendicular height of this scalene triangle. I have no angles provided.      Log On


   

Question 966925: I have a base length of 23.73m. A long side of 16.38m and a short side of 16.33m. May you help me find the perpendicular height of this scalene triangle. I have no angles provided. Thankyou.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You should make a drawing to more clearly understand.

Angle between long side and base side:
23.73%5E2%2B16.38%5E2-2%2A%2823.73%29%2816.38%29cos%28s%29=16.33%5E2----this is Law of Cosines.
-2%2823.73%29%2816.38%29cos%28s%29=16.33%5E2-23.73%5E2-16.38%5E2
cos%28s%29=%2816.33%5E2-23.73%5E2-16.38%5E2%29%2F%28-2%2823.73%29%2816.38%29%29
cos%28s%29=%2823.73%5E2%2B16.38%5E2-16.33%5E2%29%2F%282%2823.73%29%2816.38%29%29
cos%28s%29=564.7484%2F777.3948
cos%28s%29=0.7264628
-
Find the SINE of s:
sin%5E2%28s%29%2Bcos%5E2%28s%29=1
sin%5E2%28s%29=1-cos%5E2%28s%29
sin%28s%29=sqrt%281-cos%5E2%28s%29%29
sin%28s%29=sqrt%281-%280.7264628%29%5E2%29
highlight_green%28sin%28s%29=0.6872%29

Height from top of triangle to the base length 23.73 is this:
16.38%2Asin%28s%29
highlight_green%2816.38%2A%280.6872%29%29
highlight%2811.26%29