Find the value of a and the area of the triangle. Round to the nearest hundredth

a = 6.65

Area = 15.84

Step-by-step explanation:

By cosine rule in the given triangle,

BC² = AC² + AB² - 2(AC)(AB)cos(C)

a² = 5² + 9²- 2(5)(7)cos(28°)

a² = 25 + 81 - 61.81

a =

a = 6.65

Area of a triangle with given three sides =

Here, s = Average of lengths of all sides

a, b and c are the measures of the respective sides of the triangle.

s =

s = 9.325

a = 6.65, b = 5 and c = 7

Now substitute these values in the formula to get the area,

Area =

        =

        =

        = 15.838

        = 15.84

2x^2+5x+17

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solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.