△HFM∼△PST

Mathematics

1 answer:

loris [4]3 years ago

6 0

Answer:

The perimeter of △HFM is 50.75 units

Step-by-step explanation:

<u><em>The correct picture of the question in the attached figure</em></u>

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor

we have

△HFM∼△PST ----> given problem

step 1

Find the scale factor

Let

z ----> the scale factor

$z=\frac{HF}{PS}$

substitute the given values

$z=\frac{14}{8}=1.75$

step 2

Find the perimeter of triangle PST

Remember that the perimeter of a triangle is the sum of its three length sides

$P=8+9+12=29\ units$

step 3

Find the perimeter of triangle HFM

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

The perimeter of triangle HFM is equal to the perimeter of triangle PST multiplied by the scale factor

$29(1.75)=50.75\ units$

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a student walks 50m on a bearing 0.25 degrees and then 200m due east how far is she from her starting point.

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Answer:

Step-by-step explanation:

I'm going to use Physics here for this concept of vectors. Here are some stipulations I have set for the problem (aka rules I set and then followed throughout the problem):

** I am counting the 50 m as 2 significant digits even though it is only 1, and I am counting 200 as 3 significant digits even though it is only 1. 1 sig dig doesn't really give us enough accuracy, in my opinion.

** A bearing of .25 degrees is measured from the North and goes clockwise; that means that measured from the x axis, the angle is 89.75 degrees. This is the angle that is used in place of the bearing of .25 degrees.

** Due east has an angle measure of 0 degrees

Now let's begin.

We need to find the x and y components of both of these vectors. I am going to call the first vector A and the second B, while the resultant vector will be C. Starting with the x components of A and B:

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