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
To find out the distance the man drove northward initially, we can use the concept of right-angled triangles.
Let's break down the information we have:
1. The man initially drove northward.
2. He then turned left and drove 10 km.
3. He turned left again and drove 20 km.
4. He found himself 10 km west of his starting point.
From this, we can see that the final position is 10 km west of the starting point. This forms the horizontal side of a right-angled triangle. Let's label it as "10 km."
Now, we know that the man initially drove northward before making any turns. Since he ended up west of his starting point, we can conclude that the northward distance he initially drove is the vertical side of the right-angled triangle.
To find the northward distance, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of its two legs.
So, using the theorem, we can set up the equation:
(northward distance)^2 + (horizontal distance)^2 = (total distance)^2
Let's solve for the northward distance:
(northward distance)^2 + (10 km)^2 = (20 km)^2
(northward distance)^2 + 100 km^2 = 400 km^2
(northward distance)^2 = 400 km^2 - 100 km^2
(northward distance)^2 = 300 km^2
northward distance = √(300 km^2)
northward distance ≈ 17.32 km (rounded to two decimal places)
Therefore, the man initially drove approximately 17.32 km northward.