Find the area of ΔABC.

A)

18.6

B)

37.20

C)

29.77

D)

21.93

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DWRead DWRead · Answer 1 · 2021-02-16T19:29:24+01:00

Answer:

Step-by-step explanation:

You know two sides of the triangle and the angle between them, so use the Law of Cosines to solve the triangle.

a² = √(b²+c² - 2bc·cosA)

= √(9²+7.8² - 2·9·7.8·cos(32°)

≅ 4.8

Then use Heron's formula to calculate the area.

semiperimeter s = 0.5×(a+b+c) ≅ 10.8

area = √(s-(s-a)(s-b)(s-c)) ≅ 18.6 square units

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bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 2 · 2022-07-23T09:54:54+02:00

The area of ΔABC is 18.6 square units. Therefore, option A is the correct answer.

In the given ΔABC, AB=7.8, AC=9 and ∠BAC=32°.

The trigonometric formula to find the area of a triangle is AreaΔ = ½ bc sin A.

Now, use AreaΔ = ½ bc sin A

=½×7.8×9 sin32°

=7.8×4.5×0.5299=18.599≈18.6

The area of ΔABC is 18.6 square units. Therefore, option A is the correct answer.

To learn more about the area of the triangle visit:

https://brainly.com/question/27683633.

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