Two forest service watchtowers spot a fire in the distance. The fire is 27 miles from Tower 2. About how far apart are the two watchtowers? 27 degree angle
To find the distance between the two watchtowers, we need to use the angle and the given distance from one watchtower to the fire.
Assuming the two watchtowers are at the same elevation level, we can use trigonometry to determine the distance between them.
Let's call the distance between the two watchtowers "x".
In this case, we have a right triangle where the distance from Tower 2 to the fire is the side adjacent to the angle of 27 degrees, and the distance between the two watchtowers (x) is the hypotenuse.
We can use the trigonometric function cosine to find x. The formula we'll use is:
cos(angle) = adjacent/hypotenuse
In this case:
cos(27 degrees) = 27 miles / x
To solve for x, we'll rearrange the equation as follows:
x = 27 miles / cos(27 degrees)
Now we can use a calculator to find the value of cos(27 degrees). Using a scientific calculator, we find that cos(27 degrees) is approximately 0.891007.
Now, we can substitute this value into the equation:
x = 27 miles / 0.891007
When we calculate it, we find that the distance between the two watchtowers is approximately 30.29 miles.
Therefore, the two watchtowers are approximately 30.29 miles apart.