Question

Given: ​ △ABC ​ with side lengths a, b, and c, and height h

Answer 1

Answer with explanation:

Given: In △ABC ​ with side lengths a, b, and c, and height h, a vertical line extends from angle B perpendicular to side b.

To prove:→ Area(ΔABC)

                              $=\frac{1}{2}\times ab \sin C$

Proof:

In △ABC ​ with side lengths a, b, and c, and height h ,

Area of ΔABC

                  $=\frac{1}{2}\times {\text{Base} \times {\text{height}$

Let perpendicular from angle , B on the side AC cuts AC at M.

   Definition of sine

$\sin {\text{theta}}=\frac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\sin C=\frac{BM}{BC}\\\\ \sin C=\frac{h}{a}\\\\h=a\sin C$

Area of Triangle ΔABC

                  $=\frac{1}{2}\times b \times h\\\\=\frac{1}{2}\times b \times a \times \sin C$

                           -----Using Substitution Property,that is , h=a sin C

→Area = 1/2 b h          

Answer 2

Answer:

h/c, csin(B), 1/2acsin(B)

Step-by-step explanation:

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