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