Question

Given: triangle ABC with side lengths a, b, and c, and height h
Prove: Area = 1/2absin C

Answer 1

Explanation:

Statements Reasons

1). ΔABC with side lengths a, b, c, and h 1). Given

2). Area =
`(1)/(2)bh` 2). Triangle area formula

3).
`\text{sin}C=(h)/(a)` 3). Definition of sine

4). asin(C) = h 4). Multiplication property of

equality.

5). Area =
`(1)/(2)ba\text{sin}C` 5). Substitution property

6). Area =
`(1)/(2)ab\text{sin}C` 6). Commutative property of

multiplication.

Hence, proved.