Question

andre and clare are discussing triangle abc that has a right angle at c and a hypotenuse of length 15 units. andre thinks the triangle could have legs that are 9 and 12 units long. clare thinks angle b could be 20 degrees and then side bc would be 14.1 units long. do you agree with either of them? i only agree with andre. i agree with both andre and clare. i only agree with clare. i dont agree with andre or clare. explain or show your reasoning.

Explanation:

Step1: Verificar André's claim

Usando el Teorema de Pitágoras: \(a^2 + b^2 = c^2\), donde \(c = 15\), \(a = 9\), \(b = 12\).
\(9^2 + 12^2 = 81 + 144 = 225\), y \(15^2 = 225\). Entonces, \(9^2 + 12^2 = 15^2\), así que André es correcto.

Step2: Verificar Clare's claim

En un triángulo rectángulo en \(C\), \(\cos(B)=\frac{BC}{AB}\) (donde \(AB = 15\) es la hipotenusa). Si \(B = 20^\circ\), entonces \(BC = AB \cdot \cos(20^\circ)\).
\(\cos(20^\circ)\approx0.9397\), así que \(BC\approx15 \cdot 0.9397\approx14.0955\approx14.1\). Entonces, Clare es correcta.

Answer:

I agree with both Andre and Clare.