Question

Trigonometry

Objective: Use trigonometry functions to find the area of triangles.
In ΔABC, AB=19, AC=24, and in m< Δ=65*. Find the area of ΔABC to the nearest tenth of a square unit.

Answer 1

206.6 units²

Step-by-step explanation:

Area = ½ × AB × AC × sin(A)

= ½ × 19 × 24 × sin(65)

= 206.6381754444

Answer 2

The area of the triangle ABC is 207.5 square units.

Step-by-step explanation:

The measurements of the sides of the triangle are
`AB=19`,
`AC=24` and
`m\angle A=65^(\circ)`

We need to determine the area of the triangle ABC.

Area of the triangle:

The area of the triangle can be determined using the formula,

`{Area}=(1)/(2) b c \sin A`

where
`b=19`,
`c=24` and
`m\angle A=65^(\circ)`

Substituting these values in the above formula, we get,

`{Area}=(1)/(2)(19)(24) \sin 65^(\circ)`

Simplifying the values, we get,

`{Area}=(1)/(2)(456) (0.91)`

`{Area}=(1)/(2)(414.96)`

`{Area}=207.48`

Rounding off to the nearest tenth, we get,

`{Area}=207.5`

Thus, the area of the triangle ABC is 207.5 square units.