I'm doing Similarities in class and have no idea how this question works. Any explanations as to how to do this question would be great. Here it is:
Here is a way to find (roughly) the width of a river without crossing it.
Place a stake B on one bank opposite a landmark A on the other bank. Walk a distance of 5m along the bank at right abgles to AB and place another stake C. Walk another 1m in the same direction and place another stake D. Now walk at right angles to BD until A and C are in line, then place a stake E. The width of the river is five times the distance between D and E. Draw a diagram showing this and explain why it works.
I assume you drew it.
Now angle ABC = angle EDC (both right angles)
and Angle ACB = angle ECD (opposite angles)
By the way that means angle BAC=angleDEC because they are complementary to equal angles
Therefore I claim the triangle CDE is similar to triangle CBA
Therefore AB/BC=DE/DC because they are corresponding parts of similar shapes
so
AB/5 = DE/1
or
AB = 5 DE
So if I measure DE I know AB without swimming
Here is a way to find (roughly) the width of a river without crossing it.
Place a stake B on one bank opposite a landmark A on the other bank. Walk a distance of 5m along the bank at right abgles to AB and place another stake C. Walk another 1m in the same direction and place another stake D. Now walk at right angles to BD until A and C are in line, then place a stake E. The width of the river is five times the distance between D and E. Draw a diagram showing this and explain why it works.
..............A
--------------*-------------------------
..............l.*
..............l...*
..............l.....*....C
..............l.......*../
--------------*---------*.*D
..............B...........*E
BC = 5, CD = 1
Triangles ABC and EDC are similar.
Therefore, AB/DE = BC/CD
Since, BC = 5 and CD = 1, AB = 5DE.
To solve this "Similarities" question, you need to follow the given instructions:
1. Place stake B on one bank of the river, opposite landmark A on the other bank.
2. Walk a distance of 5m along the bank at right angles to AB and place another stake C.
3. Walk another 1m in the same direction and place another stake D.
4. Walk at right angles to BD until A and C are in line, then place a stake E.
To understand why this method works, let's explain it step by step:
Step 1: Place stake B on one bank opposite landmark A on the other bank. This step helps establish a known reference point on each side of the river.
Step 2: Walk a distance of 5m along the bank at right angles to AB and place stake C. By moving perpendicular to the AB line, you create a baseline that will help determine the width of the river.
Step 3: Walk another 1m in the same direction and place stake D. This additional movement ensures that stake D is not right next to stake C and adds a distance component to the calculation.
Step 4: Walk at right angles to BD until A and C are in line, then place stake E. This step involves aligning stakes A, B, and C in a straight line. By ensuring that A, B, and C are collinear, you create a right-angled triangle (ABE) where stake E represents the height or width of the river.
The width of the river can be determined by comparing the distance between stakes D and E. According to the instructions, the width of the river is five times the distance between stake D and stake E.
By multiplying the distance between D and E by 5, you can approximate the width of the river without having to cross it.
It is worth mentioning that drawing a diagram will visually represent the situation and help you understand the method better.