Solve the given problems. Sketch an appropriate figure,...

Solve the given problems. Sketch an appropriate figure, unless the figure is given. An antenna was on the top of the World Trade Center (before it was destroyed in 2001 ). From a point on the river 7800 ft from the Center, the angles of elevation of the top and bottom of the antenna were $12.1^{\circ}$ and $9.9^{\circ},$ respectively. How tall was the antenna? (Disregard the small part of the antenna near the base that could not be seen.) The former World Trade Center is shown in Fig. 4.61

Solve the given problems. Sketch an appropriate figure, unless the figure is given.
An antenna was on the top of the World Trade Center (before it was destroyed in 2001 ). From a point on the river 7800 ft from the Center, the angles of elevation of the top and bottom of the antenna were $12.1^{\circ}$ and $9.9^{\circ},$ respectively. How tall was the antenna? (Disregard the small part of the antenna near the base that could not be seen.) The former World Trade Center is shown in Fig. 4.61

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Key Concepts

Tangent Function

The tangent function is a trigonometric ratio that relates the opposite side to the adjacent side of a right triangle. It is particularly useful in problems involving angles of elevation or depression, where one can find the height of an object given the horizontal distance and the angle measured from the horizontal to the object.

Angle of Elevation

The angle of elevation is defined as the angle above the horizontal line from a given observation point to an object. It is a crucial concept in solving problems involving heights and distances, as it allows the use of trigonometric relationships to determine vertical heights when the horizontal distance is known.

Right Triangle Geometry

Right triangle geometry deals with triangles that contain a 90-degree angle, enabling the use of trigonometric ratios such as sine, cosine, and tangent to relate the sides and angles. This framework is essential for understanding and solving problems where one calculates unknown lengths or heights from known angles and distances.

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