Question

NO LINKS!!! URGENT HELP PLEASE!!!

The distance between Miami, Florida and Bermuda is about 1042 miles. The distance from Bermuda to San Juan. Puerto Rico is about 965 miles, and the distance from San Juan to Miami is about 1038 miles. Find the area of the triangle formed by the three locations.

Answer 1

444,523.45 square miles (2 d.p.)

Explanation:

To find the area of a triangle formed by the locations of Miami, Bermuda, and San Juan, use Heron's formula.

`\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=√(s(s-a)(s-b)(s-c))$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}`

Label the three sides of the triangle as 'a', 'b', and 'c', where 'a' is the distance from Miami to Bermuda (1042 miles), 'b' is the distance from Bermuda to San Juan (965 miles), and 'c' is the distance from San Juan to Miami (1038 miles):

• a = 1042 miles
• b = 965 miles
• c = 1038 miles

To find the half perimeter, s, half the sum of the three side lengths:

`\implies s=(a+b+c)/(2)=(1042+965+1038)/(2)=1522.5`

Substitute the values of a, b, c and s into Heron's formula and solve for area, A:

`\begin{aligned}A&=√(s(s-a)(s-b)(s-c))\\&=√(1522.5(1522.5-1042)(1522.5-965)(1522.5-1038))\\&=√(1522.5(480.5)(557.5)(484.5))\\&=444523.4468348...\\&=444523.45\; \sf miles^2\;(2\;d.p.)\end{aligned}`

Therefore, the area of the triangle formed by the three locations is 444,523.45 square miles, to two decimal places.

Answer 2

444523.45 square miles

Explanation:

By using Heron's formula, we can easily find the area of the triangle formed by Miami, Bermuda, and San Juan, we need to use the lengths of the three sides of the triangle.

Let,

Side a: Distance from Miami to Bermuda = 1042 miles

Side b: Distance from Bermuda to San Juan = 965 miles

Side c: Distance from San Juan to Miami = 1038 miles

Now we can use Heron's formula to find the area of the triangle:

s =
`(a+b+c)/(2)`

s =
`(1042 + 965 + 1038)/(2)=1522.5` miles

A =
`√(s(s-a)(s-b)(s-c))`

A =
`√(1522.5(1522.5-1042)(1522.5-965)(1522.5-1038))=444523.45`

Therefore, the area of the triangle formed by Miami, Bermuda, and San Juan is approximately 444523.45 square miles.