Question

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

A = 79°, b = 77, c = 41

Answer 1

1549.5

Explanation:

Hello There!

Heron's area formula is

`A=((a)(b)sin(c))/(2)`

all we have to do is plug in the values

so

`A=(77*41sin79)/(2) \\77*41=3157\\3157sin79=3098.997018\\(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

Answer 2

• 1549.24

Explanation:

Heron's Area formula:

• A =
  `√(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.

Use the law of cosines to find the missing side:

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

Now find the value of s:

• s = 1/2(80 + 77 + 41) = 99

Find the area:

• A =
  `√(99(99 - 80)(99 - 77)(99 - 41))` =
  `√(2400156)` = 1549.24