Question

Solve each problem. See Examples 3 and 4. Height of an Antenna A scanner antenna is on top of the center of a house. The angle of elevation from a point 28.0 m from the center of the ho​​use to the top of the antenna is 27°10', and the angle of elevation to the bottom of the antenna is 18°10'. Find the height of the antenna.

Accepted Answer

Identify the points involved: the point on the ground 28.0 m from the house center, the bottom of the antenna (top of the house), and the top of the antenna. The horizontal distance from the observation point to the house center is 28.0 m. Convert the given angles from degrees and minutes to decimal degrees or use them as is in trigonometric functions. For example, 27°10' means 27 degrees and 10 minutes, where 1 minute = 1/60 degrees. Use the tangent function, which relates the angle of elevation to the opposite side (height) and adjacent side (horizontal distance). For the bottom of the antenna (top of the house), set up the equation: $$	an(18$$^{\circ}$$10') = \frac{h_{house}}{28.0}$$, where $$h_{house} is $$the height of the house. Similarly, for the top of the antenna, set up the equation: $$	an(27$$^{\circ}$$10') = \frac{h_{house} + h_{antenna}}{28.0}$$, where $$h_{antenna} is $$the height of the antenna. Solve the first equation for $$h_{house}$$, then substitute into the second equation to solve for $$h_{house} + h_{antenna}. $$Finally, subtract $$h_{house}$$ from this result to find the height of the antenna: $$h_{antenna} = (h_{house} + h_{antenna}) - h_{house}.$$

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Angle of Elevation

Right Triangle Trigonometry

Difference of Heights Using Angles