He sees Kristen at a 65 degree angle of elevation and Greg

[Guest]

"Greg and Kristine are on opposite ends of a zip line that crosses a gorge. Greg went across the gorge first, and he's now on a ledge that's 15 m above the bottom of the gorge. Kristen is at the top of a cliff that is 72 m above the bottom of the gorge. Jon is on the ground at the bottom of the gorge, below the zip line. He sees Kristen at a 65 degree angle of elevation and Greg at a 35 degree angle of elevation,. What is the width of the gorge to the nearest metre?"

Answer: 55 m.

[Baltuilhe]

Good night!

Captura de Tela 2018-12-29 às 22.50.42.png (95.92 KiB) Viewed 2846 times

Accondingly to drawing:
[tex]\tan 35^{\circ}=\dfrac{15}{x}\\\tan 65^{\circ}=\dfrac{72}{y}\\w=x+y\\w=\dfrac{15}{\tan 35^{\circ}}+\dfrac{72}{\tan 65^{\circ}}\approx 21,42+33,57\\\boxed{w\approx 55,00}[/tex]

I Hope I have helped!