Question

EXAMEN DEL SEGUNDO PARCIAL DE GEOMETRÍA Y TRIGONOMETRÍA/ayuda Pls

Answer 1

Hola!

Explicación paso a paso:

■》Solución: Deduzco que son triángulos rectángulos, por lo tanto aplicamos el teorema de Pitágoras para calcular la .medida del lado que falta...

1)

${c}^{2} = {(8 \: cm)}^{2} + {(6 \: cm)}^{2} \\ {c}^{2} = 64 \: {cm}^{2} + {36 \: cm}^{2} \\ {c}^{2} = 100 \: {cm}^{2} \\ c = \sqrt{100 \: {cm}^{2} } \\ c = 10 \: cm$

2)

${c}^{2} = {a}^{2} + {b}^{2} \\ {(12 \: cm)}^{2} = {(6 \: cm)}^{2} + {b}^{2} \\ 144 \: {cm}^{2} - 36 \: {cm}^{2} = {b}^{2} \\ 108 \: {cm}^{2} = {b}^{2} \\ \sqrt{108 \: {cm}^{2} } = b \\ \sqrt{36 \times 3 \: {cm}^{2} } \\ 6 \sqrt{3} \: cm = b \\ b = 6 \sqrt{3} \: cm$

3)

${c}^{2} = {a}^{2} + {b}^{2} \\ {15 \: cm}^{2} = {a}^{2} + {(7.5 \: cm)}^{2} \\ 225 \: {cm}^{2} - \frac{225}{4} \: {cm}^{2} = {a}^{2} \\ 168.75 \: {cm}^{2} = {a}^{2} \\ \sqrt{168.75 \: {cm}^{2} } = a \\ 13 \: cm = a \\ a = 13 \: cm$

4)

${c}^{2} = {a}^{2} + {b}^{2} \\ {(18 \: cm)}^{2} = {a}^{2} + {(5.5 \: cm)}^{2} \\ 324 \: {cm}^{2} - 30.25 \: {cm}^{2} = {a}^{2} \\ 293.75 \: {cm}^{2} = {a}^{2} \\ \sqrt{293.75 \: {cm}^{2} } =a\\ 17.14 \: cm = a \\ a = 17.14 \: cm$