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 ?

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,

In triangle DEB,

[from (i)]

feet

From equation (iii) the height of the tree is

AB=6+126=132 feet.

Hence, the height of the tree is 132 feet.

sina-sinb

cosb+cosa

tana-tanb

cos0+cos x pi/3

20tan

step-by-step explanation:

we can't see all full 4 options, but if this is the full option, than the very left one is correct:

-2/5 * -3 3/4

remake the question, adding a picture of all the question, or write down the full left and right answers.