Question

if the area of angles abc =36 square units and a=c=12, what is obtuse angle c?

Answer 1

Triangle ABC has sides a = c = 12
The base is side b , opposite the obtuse angle B

     Area = (½) • b • h = 36  ...  b = base , h = height
        h = 72 ⁄ b

        (b ⁄ 2)² + h² = 12² ... Pythagorean Theorem

      (b² ⁄ 4) + (72 ⁄ b)² = 144 ... substituted for "h"

    (b² ⁄ 4) + (5184) ⁄ b² = 144 ... multiply by 4b²

         (b^4) + 4(5184) = 4(144)b²

 (b^4) − (576)b² + (20736) = 0 ... "u" substitution

   u² − (576)u + (20736) = 0 ... quadratic solution

        u = 288 ± 249.415

 u = b² = 537.415      and   u = b² = 38.585
    b = 23.18           b = 6.212

Since the angle opposite the base (angle B) is obtuse then b > "a" or "c"

  so ... b = 23.18

and using the Law of Cosines:

        b² = a² + c² − 2 • a • c • cos[B]
     (23.18)² = (12)² + (12)² − 2 • (12) • (12) • cos[B]
     cos[B] = -0.866
    B = 150º

Answer 2

thank but can i also use this as c?

Answer 3

yeah sorry its C instead of B in the last 3 lines

Answer 4

ok thank you so much :)

Answer 5

C= angle B because its opposite side C