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In the figure, angles $\angle ABC$ and $\angle AST$ are right angles. If $AC = 35,$ then what is $AS$?

 Apr 6, 2024

Best Answer 

 #3
avatar+214 
+1

So then here is my explanation: 

To find the length of segment AS in triangle AST.

You have information about the lengths of AC, AT, and BT.

Using the Pythagorean theorem, you calculate BC as √(AC² - AB²), which is √(35² - 20²) = √825.

Then, you find CT by adding BC and TB:

CT² = BC² + TB²

= 825 + 9²

= 906.

Now, you use the Pythagorean theorem for triangle CST to get CS² + ST² = CT² = 906.

And for triangle AST, you have AS² + ST² = AT², which is 121.

Subtracting equation 1 from equation 2, you get

AS² - CS² = -785.

Rearrange to get :

AS² - (35 - AS)² = -785.

Further simplify to AS² - AS² + 70AS - 35² = -785.

Now, solve for AS, and you get AS ≈ 6.28.

So, the length of segment AS is approximately 6.28 units.

 #1
avatar+214 
+1

Um, is there an image to this question, becuase I have no idea without any image. smiley

 #2
avatar+214 
+1

I think there might be some things missing but I heard of the question, and I think it is:

In the figure, angles ABC and AST are right angles. If AC = 35, AT = 11, and BT = 9, then what is AS?

 #3
avatar+214 
+1
Best Answer

So then here is my explanation: 

To find the length of segment AS in triangle AST.

You have information about the lengths of AC, AT, and BT.

Using the Pythagorean theorem, you calculate BC as √(AC² - AB²), which is √(35² - 20²) = √825.

Then, you find CT by adding BC and TB:

CT² = BC² + TB²

= 825 + 9²

= 906.

Now, you use the Pythagorean theorem for triangle CST to get CS² + ST² = CT² = 906.

And for triangle AST, you have AS² + ST² = AT², which is 121.

Subtracting equation 1 from equation 2, you get

AS² - CS² = -785.

Rearrange to get :

AS² - (35 - AS)² = -785.

Further simplify to AS² - AS² + 70AS - 35² = -785.

Now, solve for AS, and you get AS ≈ 6.28.

So, the length of segment AS is approximately 6.28 units.

 #4
avatar+214 
+1

This is a nice question smileycoolsmiley, kind of challenging.


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