Mathematics: Standing 140 feet from the base of a tree, Alejandro uses his clinometer to site the top of the tree. The reading on his clinometer is 42 degrees. If his eyes are 6 feet above the ground, how tall is the building ?

100x 0.18 as it equals 18 when you multiply it ...

Standing 140 feet from the base of a tree, Alejandro

kirstenb278

12.02.2022

132 feet

Step-by-step explanation:

Given that Alejandro is standing at a distance of 140 feet from the base of the tree and his eyes are 6 feet above the ground.

Let AB is the height of the tree and point E is the location of his eyes which is 6 feet above from C on the ground as shown in the figure.

The distance between points A and C, AC=140 feet.

Drawing a horizontal line from point E which meets AB at point D as shown.

As ACED forms a rectangle, so

AC=DE=140 feet ...(i)

CE=AD= 6 feet ...(ii)

The height of the tree, AB=AD+DB

By using equation (ii), AB=6+DB ...(iii)

Now, given that the on watching the top of the tree, the reading on the clinometer is 42 degrees.

So, $\angle DEB = 42^{\circ}$

In triangle DEB,

$\tan 42^{\circ} = \frac {DB}{DE} \\\\\Rightarrow DB = DE \times \tan 42^{\circ} \\\\$

$\Rightarrow DB = 140 \times \tan 42^{\circ}$ [from (i)]

$\Rightarrow DB = 126$ feet

From equation (iii) the height of the tree is

AB=6+126=132 feet.

Hence, the height of the tree is 132 feet.

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