Answer:
340.63
Step-by-step explanation:
To find the area we need to calculate the height of the triangle and one of its sides. the bisector cuts the 60° angle in two of 30°. In the picture I drew the triangle and the sides we need to calculate are y and h.
[tex]\angle C = 180-45-60= 75.[/tex]
[tex]\angle ACT = 180-30-75 = 75.[/tex]
We are going to calculate x, y and h with sin law:
[tex]\frac{x}{sin(75)}= \frac{24}{sin(75)}[/tex]
[tex]x= \frac{24*sin(75)}{sin(75)}=24.[/tex]
[tex]\frac{y}{sin(60)}= \frac{24}{sin(45)}[/tex]
[tex]y= \frac{24*sin(60)}{sin(75)}=29.39.[/tex]
[tex]\frac{h}{sin(75)}= \frac{24}{sin(90)}[/tex]
[tex]h= \frac{24*sin(75)}{sin(90)}=23.18.[/tex]
Then, the area of the triangle is
A = [tex]\frac{y*h}{2} = \frac{29.39*23.18}{2}= 340.63.[/tex]
