Question

As part of an art installation, Larry wants to tie a piece of rope from the end of a 10m branch that is sticking out of the ground at 23.58 degrees angle to the end of a 1 m tall stake that is 4 m west of the end of the branch. The plans for the installation are shown below. Answer the questions below:1. How many meters above the ground is the end of the branch?2. What is the shortest possible rope length (in meters) that Larry can use to attach the end of the branch to the top of the stake?

Answer 1

Given data:

The length of branch is BC=10 m.

The given angle is β=23.58 degrees.

1)

The expression for the height of the branch above the ground is,

$h=BC(\sin \beta)$

Substitute the given values in the above expression.

$\begin{gathered} h=(10m)(sin(23.58^{\circ})) \\ =4m\text{ } \end{gathered}$

Thus, the height of the branch above the ground is 4 m.