Two honey bees X and Y leave the hive H at the same time.X flies 29 m due south and Y flies 11 m on a bearing of 113degree.how far apart are they?(use same scale?)
South heading is 180 degrees
180 - 113 = 67 degrees apart
sides of triangle = 11 and 29 with 67 deg between
law of cosines
x^2 = 11^2 + 29^2 - 2*11*29cos 67
To find the distance between bees X and Y, we can use trigonometry.
Step 1: Draw a diagram of the situation. Label the starting point of both bees as H. The 29 m distance traveled by bee X will be directly south, and the 11 m distance traveled by bee Y will be at a bearing of 113 degrees from the starting point.
Step 2: Draw a right-angled triangle where the starting point H is the right angle. The line connecting H to bee X will be the base, and the line connecting H to bee Y will be the adjacent side.
Step 3: Now we can use trigonometric functions to find the length of the hypotenuse, which represents the distance between X and Y. We know the adjacent side (11 m) and the angle between the adjacent side and the hypotenuse (113 degrees).
Step 4: Since we know the adjacent side and the angle, we can use the cosine function to find the length of the hypotenuse. The cosine function can be written as:
cos(angle) = adjacent / hypotenuse
Rearranging the formula to solve for the hypotenuse:
hypotenuse = adjacent / cos(angle)
Step 5: Plug in the values into the formula:
hypotenuse = 11 / cos(113 degrees)
Step 6: Calculate the value using a scientific calculator or online trigonometry calculator.
hypotenuse ≈ 23.116 m (rounded to three decimal places)
Therefore, the distance between bees X and Y is approximately 23.116 meters.