Answer:
Pythagoras's theorem
Step-by-step explanation:
In the given drawing, there are three right triangles (two smaller triangles formed inside one right triangle), which are;
1) The smallest right triangle with side lengths 'b', 'f', and 'd'
2) The intermediate right triangle with side lengths 'f', 'a' and 'c - d'
3) The right triangle ΔABC containing the other two with side lengths, 'a', 'b', 'c'
By trigonometric ratio we have;
1/cos(B) = a/(c - d) = c/a
By cross multiplication, we get
a² = c² - c·d
Similarly, we have;
The vertex angle for the small right triangle at C = ∠B
1/sin(B) = b/d = c/b
∴ b² = c·d
Therefore, adding the values of 'a²', and 'b²' together, we get;
a² + b² = c² - c·d + c·d = c²
Therefore;
a² + b² = c² which is Pythagoras's theorem.
