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lys-0071 [83]
3 years ago
7

Use Heron's Area Formula to find the area of the triangle. (Round your answer to two decimal places.)

Mathematics
2 answers:
aniked [119]3 years ago
6 0

Answer:

  • 1549.24

Step-by-step explanation:

<u>Heron's Area formula:</u>

  • A = \sqrt{s(s - a)(s - b)(s - c)}, where s is semi-perimeter
  • s = 1/2(a + b + c)

We are given two sides and the included angle.

<u>Use the law of cosines to find the missing side:</u>

  • a² = b² + c² - 2bccos A
  • a² = 77² + 41² - 2*77*41*cos 79
  • a² = 6405
  • a = 80 (rounded)

<u>Now find the value of s:</u>

  • s = 1/2(80 + 77 + 41) = 99

<u>Find the area:</u>

  • A = \sqrt{99(99 - 80)(99 - 77)(99 - 41)} = \sqrt{2400156} = 1549.24
Scrat [10]3 years ago
6 0

Answer:

1549.5

Step-by-step explanation:

Hello There!

Heron's area formula is

A=\frac{(a)(b)sin(c)}{2}

all we have to do is plug in the values

so

A=\frac{77*41sin79}{2} \\77*41=3157\\3157sin79=3098.997018\\\frac{3098.997018}{2} =1549.498509

so the area of the triangle is 1549.498509

our final step is to round to the nearest hundredth

the answer would be 1549.5

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