buck is building a horse corral with the shape and dimensions shown in the sketch. He wants to make sure the corners of the corral measure 90 degrees

how long must diagonal AC be so angle B is a right angle?

uprgigt corner is D other side is C

Downleft is A across from B
16 ft down and 12 ft side

Answer:

BxA=F

Step-by-step explanation:

Diagonal AC must be 20 feet so that ∠B will be 90°.

According to asked question, buck is creating a horse coral  by designing in such a way that corners will be at 90°.

So according to question we have to make ∠B as 90°.

So quadrilateral ABCD becomes a rectangular.

Therefore ΔABC  will be a right-angle triangle in which we can use Pythagoras theorem to measure the diagonal AC.

The Pythagoras Theorem says that in a right-angle triangle, the square of the hypotenuse is the sum of square of the other two sides of the right-angle triangle.

In the right-angle tringle ΔABC,

AC²=AB²+BC²

⇒ AC²=16²+12²

⇒ AC²=256+144=400

⇒AC=√400

⇒AC=20 feet

Therefore, Diagonal AC must be 20 feet so that ∠B will be 90°.

Learn more about Pythagoras Theorem

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