Question

Triangle ABC is an equilateral triangle with side lengths labeled a, b, and c. Triangle A B C is an equilateral triangle. The length of side A B is c, the length of B C is a, and the length of A C is b. Trigonometric area formula: Area = One-half a b sine (C) Which expressions represent the area of triangle ABC? Select three options. a c sine (60 degrees) One-half b c sine (60 degrees) One-half a squared sine (60 degrees) StartFraction a squared b sine (60 degrees) Over 2 EndFraction StartFraction a b sine (60 degrees) Over 2 EndFraction

Answer 1

Answer:

One-half b c sine (60 degrees)

One-half a squared sine (60 degrees)

StartFraction a b sine (60 degrees) Over 2 EndFraction

Explanation:

The area rule states that the area of any triangle is equal to half the product of the lengths of the two sides of the triangle multiplied by the sine of the angle included by the two sides.

From the question, Equilateral triangle refer to a triangle with equal angle and equal sides. The sum of an angle in a triangle = 180°; this implies that each angles have 60°.

∴ the three options that defines the expressions that represent the are of triangle ABC are:

One-half b c sine (60 degrees)  

i.e $\frac{1}{2}bcsin60^{0}$

One-half a squared sine (60 degrees) ; if the two opposite sides posses the same parameters.

i.e $\frac{1}{2}a^{2}sin60^{0}$

StartFraction a b sine (60 degrees) Over 2 EndFraction

i.e $\frac{absin60^{0}}{2}$

Answer 2

Answer:

choice 3= 1/2a^2sin(60)

Explanation: