Find the area of a triangle with sides lengths 17, 18, and 21.4 units. Round the answer to the nearest hundredth.
well, yes, if you plug in your numbers.
use law of cosines to find angle A
Then the area is 1/2 bc sinA
Then 1/2bc sinA is the answer? :o
To find the area of a triangle, we can use Heron's formula.
First, we need to calculate the semi-perimeter of the triangle, which is equal to half the sum of the lengths of its sides.
The semi-perimeter (s) can be calculated as:
s = (17 + 18 + 21.4)/2
Next, we can use Heron's formula to find the area (A) of the triangle. Heron's formula states that the area of a triangle with side lengths a, b, and c and semi-perimeter s is given by the formula:
A = √(s(s-a)(s-b)(s-c))
Plugging the values into the formula, we get:
A = √(s(s-17)(s-18)(s-21.4))
Now, let's calculate the values step by step.
s = (17 + 18 + 21.4)/2
= 56.4/2
= 28.2
A = √(28.2(28.2-17)(28.2-18)(28.2-21.4))
Now, we can continue with the calculations:
A = √(28.2(11.2)(10.2)(6.8))
A = √(2,841.4848)
A ≈ 53.33 (rounded to the nearest hundredth)
Therefore, the area of the triangle is approximately 53.33 square units.