A surveyor sets a stake and then walks 150 ft north, where she sets a second stake. She then walks 300 ft east and sets a third stake. How far from the first stake is the third stake? Round to the nearest tenth.
All I know is you use law of sines and subtract 300 from 150
no
make a diagram, don't you have a right-angled triangle?
so using Pythagoras, you want the hypotenuse, let it be x
x^2 = 150^2 + 300^2
= 22500 + 90000
= 112000
so x = √112500
(check my arithmetic, I was doing mental math)
To find the distance between the first stake and the third stake, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the first stake as the starting point (0, 0), the second stake as point A (0, 150), and the third stake as point B (300, 150). Point A and point B form a right triangle, with the segment connecting them being the hypotenuse.
First, we need to find the length of the horizontal side of the triangle, which is the distance between the first stake and the third stake. This can be calculated by finding the difference between the x-coordinates of point A and point B.
Since the x-coordinate of point A is 0 and the x-coordinate of point B is 300, we can subtract the two values to find the length of the horizontal side: 300 - 0 = 300 ft.
Next, we need to find the length of the vertical side of the triangle. This can be calculated by finding the difference between the y-coordinates of point A and point B.
Since the y-coordinate of point A is 150 and the y-coordinate of point B is also 150, the vertical side has no length.
Now, we can use the Pythagorean theorem to find the length of the hypotenuse, which is the distance between the first stake and the third stake.
Applying the Pythagorean theorem: hypotenuse^2 = horizontal side^2 + vertical side^2
Since the vertical side has no length, we can simplify the equation: hypotenuse^2 = horizontal side^2
Substituting the values we found: hypotenuse^2 = 300^2
Calculating the value of the hypotenuse: hypotenuse = √(300^2) = 300 ft
Therefore, the distance between the first stake and the third stake is 300 ft.