4.) Anoki wants to determine the height of a vertical lighthouse, shown below. He measures the angle of
elevation to the top of the lighthouse at a point 103 feet along level ground from the center of the base of the
lighthouse. The angle of elevation is 31º. Which of the following expressions gives the best approximation
of the height of the lighthouse, in feet?
D. 103 cos 31°
cos 31°
A.
103
tan 31°
B.
103
C. 103 sin 31°
E. 103 tan 31°
310
103

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The height of the lighthouse is 103×tan 31°.

What is Tangent (Tanθ)?

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

Given that the distance between the Anoki and the lighthouse is 103 feet, while the angle between Anoki and the top of the lighthouse is 31°. Therefore, using the tangent function of the trigonometry we can write the height of the lighthouse as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

[tex]\rm tan(31^o) = \dfrac{\text{Height of the lighthouse}}{103\ feet}\\\\\text{Height of the lighthouse} = 103 \times tan(31^o)\\\\[/tex]

Hence, the height of the lighthouse is 103×tan 31°.

Learn more about Tangent (Tanθ):

https://brainly.com/question/10623976

#SPJ2