Answer:
In the given Δ ABC
the height will be CD
sin (A) = [tex]\dfrac{P}{H}[/tex]
sin (A) = [tex]\dfrac{CD}{b}[/tex]................(1)
now to find area of the ΔABC
area of the ΔABC = [tex]\dfrac{1}{2}\times Base \times Height[/tex]
=[tex]\dfrac{1}{2}\times c \times CD[/tex]
from equation (1) we can substitute of the value of CD.
=[tex]\dfrac{1}{2}\times c \times b sin(A)[/tex]
The base of ΔABC is c then the height is CD and the area of triangle is given by: [tex]\rm \dfrac{1}{2}\times c \times b\times sin(A)[/tex]
Given :
AC = b
BC = a
c is the base of triangle ABC.
Solution :
In the given triangle ABC
[tex]\rm sin(A) = \dfrac{Perpendicular}{Hypotenuse}[/tex]
the height will be CD,
[tex]\rm sin (A) = \dfrac{CD}{b}[/tex] ----- (1)
Area of the triangle ABC
[tex]\rm = \dfrac{1}{2}\times base\times height[/tex]
[tex]\rm =\dfrac{1}{2}\times c \times CD[/tex] --- (2)
Now from equation (1) and (2) we get
[tex]\rm Area\;of\;\Delta ABC = \dfrac{1}{2}\times c \times b\times sin(A)[/tex]
For more information, refer the link given below
https://brainly.com/question/3827723
