After walking due west,turning and walking due south a man is 900 metres from his starting point and bearing 205 degrees from it.How far did he walk(a) westward?(b)southward?
I get a nice right-angled triangle with angles
25° and 65° , and hypotenuse of 900 m
W/900= cos25°
W = 900cos25 =app 815.7 m
S/900 = sin25
S = 900sin25 = appr 380.4 m
Thankyou
815.7m and 380.4m
To find how far the man walked westward and southward, we need to understand the information given and the concepts involved.
Let's break down the information given:
1. After walking due west: The man moved in a westward direction.
2. Turning and walking due south: The man changed his direction and moved southward.
3. The man is 900 meters from his starting point: This gives us the overall displacement of the man from his starting point.
4. The bearing is 205 degrees from the starting point: This provides us with the direction in which the man is currently facing.
Based on the given information, we can create a diagram to visualize the situation.
Let's assume the starting point as the origin (0,0) on a coordinate plane. After walking west, the man would be at some point (x,0). Then, after turning and walking south, the man would move to a point (x, -y).
Now, let's find the values of x and y step by step.
First, we will find the value of x:
If the man walked westward, his displacement in the x-axis is equal to the distance he walked westward. Therefore, x gives us the answer to part (a) of the question – how far did he walk westward?
Next, we will find the value of y:
Since the man moved southward, his displacement in the y-axis is equal to the distance he walked southward. So, y gives us the answer to part (b) of the question – how far did he walk southward?
To find the values of x and y, we can use trigonometry. Let's use the concept of right-angled triangles and focus on the angle of 205 degrees, which is measured from the positive x-axis.
In a right-angled triangle, the hypotenuse (H) represents the overall displacement of the man, the adjacent side (A) represents the displacement in the x-axis, and the opposite side (O) represents the displacement in the y-axis.
Using the trigonometric ratios, we have:
cosθ = A/H (where θ is the angle between the adjacent and hypotenuse)
sinθ = O/H (where θ is the angle between the opposite and hypotenuse)
In this case, θ = 205 degrees.
Using these formulas, we can rearrange them to solve for A and O:
A = H * cosθ
O = H * sinθ
Now, let's substitute the values we know:
H = 900 meters
θ = 205 degrees
Calculating A:
A = 900 * cos(205°)
Calculating O:
O = 900 * sin(205°)
After performing these calculations, we can find the values of A and O. The value of A will give us the distance walked westward (part a of the question), and the value of O will give us the distance walked southward (part b of the question).