Question

Can y’all help with geo?

Answer 1

Here's the solution,

figure 1.

by using trigonometry,

=》

$\sin(60) = \dfrac{5 \sqrt{3} }{y}$

=》

$\dfrac{ \sqrt{3} }{2} = \dfrac{5 \sqrt{3} }{y}$

=》

$\dfrac{1}{y} = \dfrac{ \sqrt{3} }{2 \times 5 \sqrt{3} }$

=》

$\dfrac{1}{y} = \dfrac{1}{10}$

=》

$y = 10$

And,

=》

$\cos(60) = \dfrac{w}{y}$

=》

$\dfrac{1}{2} = \dfrac{w}{10}$

=》

$w = 5$

So, values are :

• y = 10
• w = 5

figure 2.

Since, it's an isosceles triangle, w = y,

So, by pythagoras theorem :

=》

${w}^{2} + {y}^{2} = (7 \sqrt{2} ) {}^{2}$

=》

${w}^{2} + {w}^{2} = 98$

=》

$2 {w}^{2} = 98$

=》

${w}^{2} = 49$

=》

$w = \sqrt{49}$

=》

$w = 7$

and we know, w = y, so their values will be equal to 7 units.