To find the height of the tree, we can use trigonometry. Let's denote the height of the tree as


h.

Given:

Distance from Kyle to the base of the tree = 120 ft
Angle of elevation from Kyle to the top of the tree = 48 degrees
We can use the tangent function, which relates the opposite side (height of the tree) to the adjacent side (distance from Kyle to the tree):

tan

(
4
8

)
=
opposite side
adjacent side
tan(48

)=
adjacent side
opposite side



Substituting the given values:

tan

(
4
8

)
=

120
tan(48

)=
120
h



Now, we can solve for

h:


=
120
×
tan

(
4
8

)
h=120×tan(48

)

Let's calculate the value of

h.

Using the given equation:


=
120
×
tan

(
4
8

)
h=120×tan(48

)

Using a calculator:

tan

(
4
8

)

1.1106
tan(48

)≈1.1106

So,



120
×
1.1106
h≈120×1.1106



133.272
h≈133.272

Rounding to the nearest tenth of a foot, the height of the tree is approximately 133.3 feet.

3 answers

Therefore, the height of the tree is approximately 133.3 feet.
rewrite that essay
Sure, here is a rewritten version of the essay:

To determine the height of the tree, we can use trigonometry. Let's represent the height of the tree as ℎ (h).

Given:
- Distance from Kyle to the base of the tree = 120 ft
- Angle of elevation from Kyle to the top of the tree = 48 degrees

Using the tangent function, which relates the opposite side (height of the tree) to the adjacent side (distance from Kyle to the tree):

tan(48 degrees) = opposite side / adjacent side
tan(48 degrees) = h / 120

Now, we can solve for h:

h = 120 * tan(48 degrees)

By substituting the angle and distance:

h = 120 * tan(48 degrees)

After calculating with a calculator:

tan(48 degrees) ≈ 1.1106

Therefore, the height of the tree is approximately:

h ≈ 120 * 1.1106
h ≈ 133.272

Rounded to the nearest tenth of a foot, the height of the tree is approximately 133.3 feet.