A boy walks 6km from point p to point q on a bearing of 065 degree.he then walks to a point r,a distance of 13km on a bearing of 146 degree
A.sketch a diagram of his movement
A.calculate correct to the nearest km, the distance pr
Cannot sketch on these posts.
I'm sure you can sketch the diagram.
Then you can use the law of cosines to find
PR^2 = 6^2 + 13^2 - 2*6*13 cos89°
So you basically have a right triangle, with legs 6 and 13; figure the hypotenuse.
Yes
Oh boy, I'm not really great at sketching, but I'll give it a go! Imagine a piece of paper, and draw a point P somewhere on it. Then draw a line extending 6km at a bearing of 065 degrees from point P and label it as point Q. Next, draw another line extending 13km at a bearing of 146 degrees from point Q and label it as point R. It should kinda look like a wonky triangle. Hope that helps!
To calculate the distance PR, we can use a fancy little math trick called the Law of Cosines. The formula goes like this: c² = a² + b² - 2ab * cos(C), where c represents the side opposite to angle C.
In this case, side a is 6km, side b is 13km, and angle C is the angle between these two sides. To find angle C, we can subtract the bearing of Q (065 degrees) from the bearing of R (146 degrees). So angle C would be 146 - 65 = 81 degrees.
Now, let's plug the numbers into the formula:
PR² = 6² + 13² - 2 * 6 * 13 * cos(81)
Using a calculator to evaluate cos(81), we get:
PR² ≈ 36 + 169 - 156.743
PR² ≈ 48.257
Finally, taking the square root of 48.257, we get:
PR ≈ 6.94 (rounded to the nearest km)
So, the distance PR is approximately 7km (rounded to the nearest km).
To sketch a diagram of the boy's movement, follow these steps:
1. Draw a horizontal line segment to represent the ground. Label the starting point as "P" on the left end, and the ending point of the first leg of the journey as "Q" on the right end.
2. Draw a line segment originating from "P" and extending towards the top right at an angle of 65 degrees. Label the end point of this line segment as "A".
3. Draw another line segment originating from "A" and extending towards the bottom right at an angle of 146 degrees. Label the end point of this line segment as "R".
4. Label the distance between "P" and "Q" as 6km, and the distance between "A" and "R" as 13km.
Now, to calculate the distance PR correct to the nearest kilometer, you can use the Pythagorean theorem since triangle PAR is a right triangle:
1. Calculate the horizontal distance:
- Distance AQ = 6km * cos(65°)
- Distance AR = 13km * cos(146°)
- Distance PR = Distance AQ + Distance AR
2. Calculate the vertical distance:
- Distance QR = 13km * sin(146°)
- Distance PQ = 6km * sin(65°)
- Distance PR = Distance QR - Distance PQ
3. Use the Pythagorean theorem:
- Distance PR^2 = (Distance PR)^2 + (Distance AR)^2
4. Take the square root of both sides:
- Distance PR = sqrt((Distance PR)^2 + (Distance AR)^2)
By substituting the values and performing the calculations, you will find the distance PR correct to the nearest kilometer.
A boy walks 6km from point p to point q on a bearing of 065 degree.he then walks to a point r,a distance of 13km on a bearing of 146 degree
A.sketch a diagram of his movement
A.calculate correct to the nearest km, the distance pr
A boy walks 6km from a point Q on a bearing of 65°. He then walks to a point R, a distance of 13km, on a bearing of 146°.
(I) sketch the diagram of his movement
(ii) calculate correct to the neatest kilometer, the distance PR