Which steps would prove the circles similar?

Mathematics

1 answer:

Eddi Din [679]3 years ago

8 0

Answer:

You can translate smaller circle onto larger circle so centers line up and then dilate to prove similarity.

Step-by-step explanation:

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Find the value of x. (Picture attached.)

Svet_ta [14]

Here, triangle AEN and ALG are similar.

We know that the ratio of corresponding sides of two similar triangles are equal. So,

$\frac{21}{42} =\frac{2x-9}{(2x-9)+(x+7)}\\\\\frac{1}{2} =\frac{2x-9}{3x-2}\\\\ 3x-2=4x-18\\\\-2+18=4x-3x\\\\16=x\\\\x=16\\$

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3 years ago

Charlie is standing 45 feet from the base of 100 foot tall tree. What is the angle of elevation from him to the kite stuck on to

galben [10]

Hey. Let me help you on this one.

In order for us to solve this problem easier, let's break it apart. We can also graph the triangle so we get visual of this problem.

I drew a quick graph for you to easier understand this question. As you can see, Charlie is standing below the tree 45 feet from it, and we need to find the unknown angle measure.

Let's form a SOHCAHTOA function which you have probably already learned in your Geometry course.

First of all let's identify our sides. The side opposite of the right triangle is a Hypotenuse, and the side that's 45 feet is adjacent, since it's adjacent to the unknown angle.

We know that we need to use $Cos$ (Cosine) with negative power to it in order to solve this question, since we are looking for the unknown angle measure.

Let's form the function which $Cos$ , Hypotenuse, and Adjacent side.

$Cos^{-1} =45/100$

Now, let's solve the left part of this function

$
Cos^{-1} =0.45$

Awesome. You will need to use your calculator for this part. Find the value of 0.45 when negative Cosine is used on it.

$Cos^{-1} =0.45$
$63.25631605$

Awesome. Let's round this number to the closest tenth

$63.3$ is the rounded value we have discussed below.

Answer: 63.3 degrees is the unknown measure of the angle