SOLUTION: In ∆ABC, b=5 and c=4. The area of the triangle is 15√7/4. To the nearest tenth, calculate a and m < A (in degrees). a = 15√7/4 = 9.92157 A =?

Algebra ->  Trigonometry-basics -> SOLUTION: In ∆ABC, b=5 and c=4. The area of the triangle is 15√7/4. To the nearest tenth, calculate a and m < A (in degrees). a = 15√7/4 = 9.92157 A =?       Log On


   

Question 1135553: In ∆ABC, b=5 and c=4. The area of the triangle is 15√7/4. To the nearest tenth,
calculate a and m < A (in degrees).
a = 15√7/4 = 9.92157
A =?
Found 4 solutions by Edwin McCravy, AnlytcPhil, MathTherapy, ikleyn:
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!


Below is the completed problem.

Edwin (aka AnlytcPhil)

Answer by AnlytcPhil(1810) About Me  (Show Source):
Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

In ∆ABC, b=5 and c=4. The area of the triangle is 15√7/4. To the nearest tenth,
calculate a and m < A (in degrees).
a = 15√7/4 = 9.92157
A =?
You can use the formula for the area of a non-right triangle, with 2 (two) sides and the angle between them, known. This is: matrix%281%2C3%2C+Area%2C+%22=%22%2C+%281%2F2%29bc+%2A+Sin+%28A%29%29

Furthermore, you might notice that the formula contains 4 variables, with all but one, given.

Angle A is between sides b and c.

Answer by ikleyn(52919) About Me  (Show Source):
You can put this solution on YOUR website!
.

           This problem is to solve it in  5  (five,  FIVE)  lines. 


For any triangle, its area is half the product of the lengths of any its two sides and the sine of the angle between them.


In your case, the Area = %281%2F2%29%2Ab%2Ac%2Asin%28A%29.


Substituting your data, you have %2815%2Asqrt%287%29%29%2F4 = %281%2F2%29%2A5%2A4%2Asin%28A%29.


From here,  sin(A) = %282%2A15%2Asqrt%287%29%29%2F%284%2A5%2A4%29 = 0.992167.


Then  for angle A you have TWO possible values  m ( < A ) = 82.82°  and  m ( < A) = 180° - 82.82° = 97.08°.    ANSWER

Solved.