a man drove his car northward, then turned left and drove 10 km and again turned left and drove 20km. he found himself 10 km west of his starting point . how far did he drive northward initially
done, see your previous post under a different name
http://www.jiskha.com/display.cgi?id=1450075351
20 km
To determine how far the man drove northward initially, we need to analyze the information given.
Let's assume the man started at point A.
- The first sentence states that he drove his car northward.
- The second sentence mentions that he turned left and drove 10 km.
- The third sentence states that he turned left again and drove 20 km.
- The last sentence mentions that he found himself 10 km west of his starting point.
From this information, we can see that the total distance he moved west by turning left twice is 10 km.
Since he found himself 10 km west of point A, we can deduce that his second left turn brought him westward back to his starting point. Hence, the distance between the point where he made his second left turn and point A is also 10 km.
To calculate the total distance the man drove northward initially, we need to form a right-angled triangle. One side will represent the distance traveled northward initially, the other side will represent the distance he drove initially westward, and the hypotenuse will represent the total distance he drove.
Let's use the Pythagorean theorem to find the length of the northward side of the triangle:
a^2 + b^2 = c^2
where:
a = distance traveled northward initially
b = distance traveled initially westward
c = total distance traveled
We know b (10 km) and c (20 km) based on the information given. So let's plug in the values:
a^2 + 10^2 = 20^2
a^2 + 100 = 400
Now, we can solve for a:
a^2 = 400 - 100
a^2 = 300
Taking the square root of both sides:
a = √300
Simplifying that, we get:
a ≈ 17.32 km
Therefore, the man initially drove approximately 17.32 km northward.