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# Geometry

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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

#3
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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
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Um, is there an image to this question, becuase I have no idea without any image.

#2
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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
+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.

#4
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This is a nice question , kind of challenging.