Question

Calcule o valor de x na figura abaixo:

Answer 1

tg60° = x / z
√3 = x / z
√3z = x

tg30° = x / 10 + z
√3/3 = √3z / 10 + z
√3/3 . (10+z)  = √3z
10√3/3 + √3z/3 = √3z
30√3/3 + √3z = 3√3z
10√3 + √3z = 3√3z
10√3 = 3√3z - √3z
10√3 = 2√3z
10√3 / 2√3 = z
5√3 / √3 = z
5.3 / 3 = z
15/3 = z
z = 5

tg30° = x /  15
√3/3 = x / 15
15√3/3  = x
5√3 = x

Answer 2

Chame o cateto adjacente ao ângulo de 60º de y

$tg60^{0}=x/y$
$\sqrt{3} =x/y$
$x=y \sqrt{3}$

$tg30^{0}=x/(10+y)$
$\sqrt{3} /3=x/(10+y)$
$\sqrt{3}*(10 + y)=3*x$
$10 \sqrt{3}+y \sqrt{3} =3x$

Como y√3 = x:

$10 \sqrt{3}+x=3x$
$10 \sqrt{3}=3x-x$
$10 \sqrt{3}=2x$
$10 \sqrt{3}/2=x$
$x =(5\sqrt{3})cm$