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

2.6 m

Explanation:

In the attached diagram

Consider Triangle ABC

`\sin36^\circ =(|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 =(|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|=√(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.