Find the area of a triangle if the sides of the triangle have the lengths 849mi, 930mi, and 1301mi.
Here's my work:
a=849
b=930
c=1301
A=.5(849)(930)sinA
sin A = 394,785 mi^2
(this number doesn't seem right to me, can you explain to me what I did wrong)?
http://www.mathopenref.com/heronsformula.html
@Damon, thank you! :)
You are welcome.
how did you get sinA?
Also, the area = (bc sinA)/2, not (ab sinA)/2
849^2 = 930^2 + 1301^2 - 2*930*1301 cosA
A = 40.6°
area = b*c*sinA/2 = 930*1301*0.651/2 = 393,879
@Steve, I plugged in the numbers in the equation. I see where I went wrong. Thank you!
To find the area of a triangle given the lengths of its sides, you can use Heron's formula. Let's go through the correct steps:
1. Calculate the semi-perimeter (s) of the triangle. The semi-perimeter is half the sum of the lengths of the triangle's sides. You can calculate it using the formula: s = (a + b + c) / 2, where a, b, and c are the lengths of the sides of the triangle.
In this case, we have a = 849 mi, b = 930 mi, and c = 1301 mi. Plugging these values into the formula, we get: s = (849 + 930 + 1301) / 2 = 2090 mi.
2. Using Heron's formula, the area (A) of the triangle can be calculated using the formula: A = √(s * (s - a) * (s - b) * (s - c)).
Plugging in the values we calculated, we get: A = √(2090 * (2090 - 849) * (2090 - 930) * (2090 - 1301)).
Calculating this expression, we find: A ≈ √(2090 * 1241 * 1160 * 789) ≈ √(233,907,106,400) ≈ 483,665.12 mi².
So, the correct area of the triangle is approximately 483,665.12 square miles.
Your calculation of sin A = 394,785 mi² is incorrect because you used the formula A = 0.5 (a)(b) sin A, which is used for calculating the area of a triangle using the lengths of two sides and the included angle. However, you didn't provide any angle information in your question, so we need to use Heron's formula instead.