Given: ΔABC, AB=12, m∠A=60°,m∠C=45°, AB =8 Find the perimeter of ΔABC

The perimeter of ΔABC is 43 units

Step-by-step explanation:

An illustrative diagram is shown in the attachment below.

To find the perimeter of the triangle, we will first determine the length of the unknown sides.

First, we can determine /BC/ using the Sine rule

From Sine rule

∴

In the diagram, and

m∠A=60° and m∠C=45°

∴

To find /AC/, will first determine m∠B

m∠A + m∠B + m∠C = 180° (Sum of angles in a triangle)

60° +m∠B + 45° = 180°

m∠B + 105° = 180°

m∠B = 180° - 105°

m∠B = 75°

Also, using the sine rule

From the diagram,

Now,

The perimeter of ΔABC = /AB/ + /BC/ + /AC/

=

= 43.09 units

≅ 43 units

Hence, the perimeter of ΔABC is 43 units.

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.