Two tracking stations are on the equator 148 miles apart. a weather balloon is located on a bearing of n41°e from the western station and on bearing of n21°e from the eastern station. how far is the balloon from the western station? round to the nearest mile from the nearest station. a 404 mil b 382 mi c 413 mil d 373 mi

  A  404 mi

Step-by-step explanation:

If we designate the points of the triangle A, B, and C for the locations of the western station, eastern station, and balloon, respectively, we have the following:

  ∠CAB = 90° - 41° = 49°

  ∠CBA = 90° + 21° = 111°

  ∠ACB = 41° -21° = 20°

side "c" (opposite ∠ACB) is 148 miles

The distance we're asked to find is AC = b, the longest side of the triangle. The law of sines tells us ...

  b/sin(B) = c/sin(C)

  b = c·sin(B)/sin(C) = (148 mi)·sin(111°)/sin(20°) ≈ 403.98 mi ≈ 404 mi

x

step-by-step explanation:

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²