MHB Solve Right Triangle Problem Without Knowing Bottom Line

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To solve a right triangle problem without knowing the base length, one can use trigonometric relationships involving angles. The angle θ can be utilized to find the hypotenuse (d) with the formula d = 16/cos(θ), where 16 meters is the adjacent side. The discussion raises skepticism about the possibility of determining a numerical value for d with only the angle θ provided. Clarification is sought on how one could arrive at a solution without additional information. Understanding these trigonometric principles is essential for solving similar problems effectively.
Jacob123
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How would I have to calculate this question for an answer, a friend of mine told me he could get the answer without knowing that the bottom line was 16 meters, I can't seem to find a way that would work, I am not sure if I am missing something or he is lying.

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I'd also like to know how your friend could determine a numerical value for $d$ just knowing the angle $\theta = 0.19$ with no other information.
If he let's you know how, post back and enlighten me.

Using the angle, $\theta$, value and the 16 meters ...

$\cos{\theta} = \dfrac{16}{d} \implies d = \dfrac{16}{\cos{\theta}}$
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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