In the figure, a person standing at point A notices that the angle of elevation to the top of the antenna is 45(degrees) 30'. A second person standing 31.0 feet farther from the antenna than the person at A finds the angle of elevation to the top of the antenna to be 43(degrees) 10'. How far is the person at A from the base of the antenna? Round to the nearest whole number. **Estimating the Height of a Structure Using Similar Triangles**This educational example illustrates the method of estimating the height of a tall structure using similar triangles. The diagram shows two individuals standing on a level surface a certain distance away from a tower, which is represented as an upright metal structure.**Description of the Diagram:**1. **Characters and Baseline:** - There are two characters standing at different positions on the baseline. - The first character is closer to the tower at point \( A \). - The second character stands further away from the tower compared to the first one.2. **Tower:** - The tower is depicted as a tall, lattice structure reaching height \( h \). 3. **Lines and Triangles:** - From each character’s position, a dashed line extends to the top of the tower, representing their respective lines of sight. - The dashed lines create two triangles. The triangle formed by the first character’s line of sight is smaller, while the triangle formed by the second character’s line of sight is larger. - The triangles share the vertical side of the height of the tower \( h \), indicating that the triangles are similar by AA (Angle-Angle) similarity criterion because they both share the angle at the top of the tower and have right angles at their bases.4. **Measurements:** - Distance \( x \) represents the horizontal distance from the first character at point \( A \) to the base of the tower. - Distance \( l \) represents the larger horizontal distance from the second character to the base of the tower.**Educational Explanation:**To estimate the height \( h \) of the tower using the principles of similar triangles, observe the following relationships:- The proportion between the sides of the similar triangles can be written as: \[ \frac{h}{x} = \frac{h_1}{x_1} \] where: - \( h \) is the height of the item being measured (tower). - \( x \) is the horizontal distance from the first character to the base of the tower. - \( h_1 \) is the distance from the first character's eyes to the top of the tower, along their line of sight. - \( x_1 \) is the distance from the second character's eyes to the top of the tower, along their line of sight.

Consider the figure representing given scenario We have to find the distance x.

Answered: In the figure, a person standing at…

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.