Answer:
[tex]LW=17.5\ units[/tex]
Step-by-step explanation:
we know that
In the right triangle LAY
Find the measure of side LY applying the Pythagoras Theorem
[tex]LY^{2} =3.5^{2}+ 7.0^{2} \\ \\ LY^{2} =61.25\\ \\ LY=\sqrt{61.25}\ units[/tex]
Find the cosine of angle ALY
[tex]cos(<ALY)=\frac{LA}{LY}[/tex]
[tex]cos(<ALY)=\frac{3.5}{\sqrt{61.25}}[/tex] -----> equation A
In the right triangle LWY
[tex]cos(<ALY)=\frac{LY}{LW}[/tex]
[tex]cos(<ALY)=\frac{\sqrt{61.25}}{LW}[/tex] -----> equation B
equate equation A and equation B and solve for LW
[tex]\frac{3.5}{\sqrt{61.25}}=\frac{\sqrt{61.25}}{LW}[/tex]
[tex]LW=(\sqrt{61.25})(\sqrt{61.25})/3.5[/tex]
[tex]LW=17.5\ units[/tex]
