⦁ A hiker travels 3 km due east then 2 km on a bearing of 110°.
Solve to find:
a) Calculate how far south the hiker is from the starting point Hint: construct a right angle triangle
so, did you construct the triangle? The distance x iscan be found using
x/2 = sin20°
All angles are measured CW from +y-axis.
D = D1+D2 = 3km[90o] + 2km[110o].
D = (3*sin 90+2*sin110) + (3*cos90+2*cos110)I,
D = 4.9 - 0.684i.
The hiker is 0.684 km South of starting point.
To find how far south the hiker is from the starting point, we will construct a right-angled triangle using the given information.
First, let's start by visualizing the given information. The hiker travels 3 km due east and then 2 km on a bearing of 110°. This means that the hiker initially moves 3 km to the right (due east) and then turns 110° to the left and moves an additional 2 km.
Now, let's construct a right-angled triangle to solve the problem. Start by drawing a horizontal line to represent the initial eastward movement of 3 km. Then, draw a line from the endpoint of this line to represent the additional 2 km traveled on a bearing of 110°.
Now, you should have a right-angled triangle with one side measuring 3 km and another side measuring 2 km. We want to find the length of the side that represents the hiker's position south of the starting point.
To do this, we can use trigonometry. Specifically, we can use the sine function, which relates the lengths of the sides of a right triangle to the angle opposite the side we want to find. In this case, we can use the sine function to relate the angle of 110° to the length of the side opposite that angle (which represents the hiker's position south of the starting point).
Using the equation sin(angle) = opposite/hypotenuse, we have sin(110°) = opposite/2 km. Rearranging the equation to solve for the opposite side (the length we want to find), we get: opposite = sin(110°) * 2 km.
Now, we can plug in the values into a calculator to get the answer. Evaluating sin(110°), we find that sin(110°) ≈ 0.9397.
Finally, we calculate the distance south of the starting point: opposite = 0.9397 * 2 km ≈ 1.8794 km.
Therefore, the hiker is approximately 1.8794 km south of the starting point.