From a point O in the school compound,adeolu is 100m away on a bearing of 80m away on a bearing of S 55°W.How far apart are both boys
How did you get 160 degrees
To find out how far apart Adeolu is from the point O, we can use trigonometry and the given bearing.
Let's assume the distance between Adeolu and Point O is d.
From the information given, we know:
- Adeolu is 100m away from Point O.
- The bearing of Adeolu from Point O is S 55°W.
To solve this, we will use the triangle formed by Point O, Adeolu, and a perpendicular line from Point O to the line connecting Adeolu and Point O.
Step 1: Draw a diagram to visualize the problem.
A (Adeolu)
/ |
/ | d (distance from O to Adeolu)
/ |
O (Point O)
Step 2: Determine the angle of the triangle connecting Point O, Adeolu, and the perpendicular line.
The bearing of S 55°W means the angle between the south direction and the line connecting Point O and Adeolu is 55°.
Step 3: Split the angle S 55°W into two angles.
Since South is directly opposite North, and the bearing is measured westwards from the North direction, we can split the angle S 55°W into a South-Southwest (SSW) angle of 180° - 55° = 125°.
Step 4: Use trigonometry to calculate the distance d.
In a right-angled triangle with angle 125°, we have the adjacent side (100m) and want to find the hypotenuse (d).
Using the cosine function:
cos(125°) = adjacent / hypotenuse
cos(125°) = 100m / d
Rearranging the formula to solve for d:
d = 100m / cos(125°)
Step 5: Calculate the distance d.
Using a calculator:
d = 100m / cos(125°)
d ≈ 100m / (-0.5736)
d ≈ -174.37m
The distance between Adeolu and Point O is approximately 174.37m. Note that the negative sign indicates it is in the opposite direction to the bearing.
To find the distance between the two boys, we can use the concept of vector addition.
First, draw a diagram representing the situation. Place point O as the origin, and draw a line segment 100m long extending from O in the direction of the bearing 55°W (clockwise from due south). This represents the position of Adeolu.
Next, draw a line segment 80m long extending from Adeolu's position (end of the previous line segment) in the direction of the bearing 80°W (clockwise from due south). This represents the position of the second boy.
To find the distance between these two points, we need to find the length of the resulting line segment connecting the two points.
Using basic trigonometry, we can calculate both the horizontal and vertical components of the line segment connecting the two points.
The horizontal component can be found using the cosine function:
Horizontal component = 80m * cos(55° + 180°) = 80m * cos(235°)
The vertical component can be found using the sine function:
Vertical component = 80m * sin(55° + 180°) = 80m * sin(235°)
Now, we have the horizontal and vertical components of the line segment. To find the distance between the two boys, we can use the Pythagorean theorem:
Distance = √(horizontal component^2 + vertical component^2)
By plugging in the calculated values for the horizontal component and vertical component, we can find the distance between the two boys.
you only give one bearing.
When you decide what that is, make a sketch, then use the law of cosines to find the side opposite the angle between the bearings.