To save expenses, you would like to buy the shortest mirror that will allow you see your entire body, should the mirror be
A) Half your height B) Two-thirds your height or C)equal to your height ?
Does the answer depends on how far away from the mirror you stand?
Please I need a detailed answer urgently for my assignment ,thank you.
To determine the size of the mirror you need to see your entire body, you need to consider a few factors: your height, the distance you stand from the mirror, and the concept of similar triangles.
Let's break down the problem step by step:
1. Determine the required height of the mirror:
- Option A: Half your height
- Option B: Two-thirds your height
- Option C: Equal to your height
2. Consider the distance you stand from the mirror:
- The further away you stand from the mirror, the larger the mirror needs to be to see your entire body.
Now, let's discuss the role of similar triangles in this situation:
Similar triangles have the same shape but may be different in size. They have corresponding angles that are congruent, which allows us to set up proportions between corresponding sides.
In this scenario, we have two similar triangles: the triangle formed by your height, the distance you stand from the mirror, and the size of the mirror, and a reference triangle formed by your height and the distance to the mirror.
To determine the required size of the mirror, we can set up a proportion between the corresponding sides of the two triangles:
Mirror height / Distance to mirror = Your height / Distance to mirror
Now, let's examine each option:
A) Half your height:
- If the mirror is half your height and you stand at the same distance, the first ratio becomes: (0.5 x your height) / Distance to mirror = your height / Distance to mirror.
- This simplifies to 0.5 = 1, which is not true. Consequently, option A is incorrect.
B) Two-thirds your height:
- If the mirror is two-thirds your height and you stand at the same distance, the ratio becomes: (0.667 x your height) / Distance to mirror = your height / Distance to mirror.
- This simplifies to 0.667 = 1, which is not true. Therefore, option B is also incorrect.
C) Equal to your height:
- If the mirror is at least equal to your height, the ratio becomes: (1 x your height) / Distance to mirror = your height / Distance to mirror.
- This simplifies to 1 = 1, which is always true. Consequently, option C is correct.
Therefore, the answer is C) equal to your height, regardless of your distance from the mirror.
Please note that even with a mirror equal to your height, you may need to adjust your distance based on personal preferences and specific circumstances.