Question

Jen and Holly are on the Athletic council and want to put a blow up version on the school mascot in the parking lot. They need to tie it down.
Jen’s rope is 7.8 m long and makes an angle of 360 with the ground. Holly’s rope is 5.9 m long. The wind is really strong so they will secure both ropes to the left of the mascot. How far to the nearest tenth of a metre, is Jen from Holly?

Answer 1

Answer:

2.6 m

Step-by-step explanation:

In the attached diagram

Consider Triangle ABC

$\sin36^\circ =\dfrac{|BC|}{7.8} \\|BC|=7.8*\sin36^\circ\\|BC|=4.5847 m$

Our goal is to determine the distance of Jen (at point A) to Holly (at Point D).

In Triangle ABC

$\cos 36^\circ =\dfrac{|AC|}{7.8} \\|AC|=7.8*\cos36^\circ\\|AC|=6.3103 m$

In Triangle BDC

Applying Pythagoras Theorem

$|BD|^2=|BC|^2+|CD|^2\\5.9^2=4.5847^2+|CD|^2\\|CD|^2=5.9^2-4.5847^2\\|CD|^2=13.7905\\|CD|=\sqrt{13.7905}=3.7136 m$

Now, |AC|=|AD|+|DC|

6.3103=|AD|+3.7136

|AD|=6.3103-3.7136

|AD|=2.5967

|AD|=2.6m (correct to the nearest tenth of a metre)

The distance of Jen from Holly is 2.6m.