A student wants to estimate the height of a tree from ground level. He measures the length of its shadow as 10 m and the angle from the top of the shadow on the ground to the top of the tree as 60°. What is the height of the tree based on these measurements?

Respuesta :

Answer:

5.77 m

Explanation:

[tex]\theta=60^{\circ}[/tex]

[tex]\text{Opposite side}=10\ \text{m}[/tex]

Here we have to use the trigonometric formula of tan.

[tex]\tan\theta=\dfrac{\text{Opposite side}}{\text{Adjacent side}}\\\Rightarrow \tan60^{\circ}=\dfrac{10}{\text{Adjacent side}}\\\Rightarrow \text{Adjacent side}=\dfrac{10}{\tan60^{\circ}}\\\Rightarrow\text{Adjacent side}=5.77\ \text{m}[/tex]

The height of the tree is the adjacent side which is 5.77 m