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

Question

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
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
∘
)
=
ℎ
120
tan(48
∘
)=
120
h
​


Now, we can solve for
ℎ
h:

ℎ
=
120
×
tan
⁡
(
4
8
∘
)
h=120×tan(48
∘
)

Let's calculate the value of
ℎ
h.

Using the given equation:

ℎ
=
120
×
tan
⁡
(
4
8
∘
)
h=120×tan(48
∘
)

Using a calculator:

tan
⁡
(
4
8
∘
)
≈
1.1106
tan(48
∘
)≈1.1106

So,

ℎ
≈
120
×
1.1106
h≈120×1.1106

ℎ
≈
133.272
h≈133.272

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

Answer 1

Therefore, the height of the tree is approximately 133.3 feet.

Answer 2

rewrite that essay

Answer 3

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.