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Trigonometry equalities, inequalities and expressions  sin, cos, tan, cot
by Guest » Sat Dec 29, 2018 9:30 pm
"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.

Guest

by Baltuilhe » Sat Dec 29, 2018 9:55 pm
Good night!
 Captura de Tela 20181229 às 22.50.42.png (95.92 KiB) Viewed 542 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!

Baltuilhe

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