Question

A woman standing on a large rock at the edge of a lake is getting ready to swing from a rope that is tied to a branch that hangs over the water. The length of the rope the woman is holding is 7.3 m long. The woman hopes to land in the water at a point that is 13.7 m away from where she stands on the large rock. The angle between the point where the rope is tied and her landing spot in the water is 89°. What is the distance between the the point where the rope is tied and the point where she wants to land to the nearest tenth of a metre.

Answer 1

6.4 m

Explanation:

The image attached is a representation of the question. to the river hence the distance between the place where she landed and the rock where she was standing must be horizontal. We are now required to find the shortest vertical distance between the point where the rope was tied and the place where she wants to land.

Note that the woman used the rope to move down in

Applying the cosine rule;

`c^(2) = a^(2) + b^(2) -2ab Cos C`

`c^(2) = 13.7^(2) + 7.3^(2) - 2(13.7 *7.3) Cos 89o`

`c^(2) = 6.4 m`