Question

select all of the following that can be used to find the height of the tree

Answer 1

Let's draw the scenario to better understand the problem:

The setup appears to form a right triangle. To be able to find the height of the tree, we will be using the Tangent function:

With respect to Θ = 41°,

Adjacent = 53 Feet

Opposite = x

Therefore, the formula for x will be:

$\text{ Tangent }\Theta\text{ = }\frac{\text{ Opposite}}{\text{ Adjacent}}$$\text{ Tangent }(41^{\circ})\text{ = }\frac{\text{ x}}{\text{ 5}3}$$\text{ 53Tangent }(41^{\circ})\text{ = x}$

With respect to Θ = 49°,

Adjacent = x

Opposite = 53 Feet

Therefore, the formula for x will be:

$\text{ Tangent }\Theta\text{ = }\frac{\text{ Opposite}}{\text{ Adjacent}}$$\text{ Tangent }(49^{\circ})\text{ = }\frac{\text{ 5}3}{\text{x}}$$\text{ x = }\frac{\text{ 5}3}{\text{Tangent }(49^{\circ})}$

Therefore, the following equations can be used to find the height of the tree:

$\begin{gathered} \text{ 53Tangent }(41^{\circ})\text{ = x} \\ \text{ or} \\ \text{ x = }\frac{\text{ 5}3}{\text{Tangent }(49^{\circ})} \end{gathered}$

The answer is the 5th and 6th choice.