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5 votes
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.

2 Answers

5 votes

Answer:

206.6 units²

Step-by-step explanation:

Area = ½ × AB × AC × sin(A)

= ½ × 19 × 24 × sin(65)

= 206.6381754444

User Wayne Lo
by
7.0k points
3 votes

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.

User Aicastell
by
6.9k points
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