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DrLiangMath
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AB=3, DC=5, ∠ CAD=$45^o$, AB ⊥ BC. Find the length of AC.
It's inefficient but start by defining angle BCA to be C. Then angle CDA = 135 - C. Call x = AC. Then by Law of SinesMathTutoringByDrLiang said:
I gave two equations. The first is the Law of Sines in triangle ABC and the second is the Law of Sines in triangle ADC. Perhaps I should have stated that.MathTutoringByDrLiang said:Thank you for your response. But we still need one more equation since we have 2 variables x and C.
Klaas van Aarsen said:Hey MathTutoringByDrLiang,
Are you actually looking for an answer to this problem? Or do you have an elegant answer to share?
If the latter, then we might move this thread to the https://mathhelpboards.com/forums/challenge-questions-and-puzzles.28/ subforum.
Btw, at this time I could provide an answer, but it's rather long winded and I'm still looking for a more elegant solution.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This means that if we know the lengths of two sides of a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse.
To use the Pythagorean theorem, you will need to know the lengths of two sides of the right triangle. Once you have these values, you can plug them into the formula a^{2} + b^{2} = c^{2}, where c represents the length of the hypotenuse. Then, solve for c by taking the square root of both sides of the equation.
No, the Pythagorean theorem can only be used to find the length of the hypotenuse if you know the lengths of two sides of the triangle. If you only know the length of one side, you will need to use other geometric principles or measurements to find the length of the hypotenuse.
Yes, there are other methods for finding the length of the hypotenuse, such as using trigonometric functions or applying the Law of Cosines. These methods may be more complex and require additional information about the triangle, but they can also be useful in certain situations.
No, the Pythagorean theorem only applies to right triangles. In a non-right triangle, you will need to use other methods, such as the Law of Cosines or the Law of Sines, to find the length of the hypotenuse.