Practicing Success
A poster is on top of a building. A person is standing on the ground at a distance of 50 m from the building. The angles of elevation to the top of the poster and bottom of the poster are 45° and 30°, respectively. What is 200% of the height (in m) of the poster? |
$\frac{25}{3}(3 - \sqrt{3})$ $\frac{75}{3}(3 - \sqrt{3})$ $\frac{50}{3}(3 - \sqrt{3})$ $\frac{100}{3}(3 - \sqrt{3})$ |
$\frac{100}{3}(3 - \sqrt{3})$ |
⇒ In triangle BCD, tan \({30}^\circ\) = \(\frac{BC}{CD}\) We know that tan \({30}^\circ\) = \(\frac{1}{√3}\) and CD = 50m, ⇒ \(\frac{BC}{50}\) = \(\frac{1}{√3}\) ⇒ BC = \(\frac{50}{√3}\) or \(\frac{50√3}{3}\) Similarly in ACD tan \({45}^\circ\) = \(\frac{AC}{CD}\) ⇒ AC = AB + BC, tan \({45}^\circ\) = 1 and CD = 50m ⇒ AC = CD or AB + BC = CD Substituting the values we get, ⇒ AB + \(\frac{50√3}{3}\) = 50, ⇒ AB= 50 - \(\frac{50√3}{3}\) ⇒ AB = 50 - \(\frac{50√3}{3}\) ⇒ AB = \(\frac{50}{3}\)(3 - \(\sqrt {3 }\)) Therefore, 200% of the Poster height = \(\frac{100}{3}\)(3 - \(\sqrt {3 }\)) |