Plane geometry is the terror of many students. In this Math video lesson you will learn how trigonometric ratios in right triangles appear on the ENEM exam and you will learn how to solve questions involving sine, cosine and tangent. To download the exercise lists in PDF to practice, click on the link below. SUBSCRIBE TO THE CHANNEL AND LEAVE A LIKE to strengthen List link: https://thyagoaraujo.com/listas-de-qu... Study with me and be successful in Math. ONLINE MATHEMATICS PLATFORM: https://www.thyagoaraujo.com Follow us on social media: ► Instagram: / escoladenumeros ► Twitter: / escoladenumeros Solved questions from previous ENEM exams 01. (ENEM-2010) An atmospheric balloon, launched in Bauru (343 kilometers northwest of São Paulo), on the night of last Sunday, fell this Monday in Cuiabá Paulista, in the region of Presidente Prudente, frightening farmers in the region. The artifact is part of the Hibiscus Project program, developed by Brazil, France, Argentina, England and Italy, to measure the behavior of the ozone layer, and its descent occurred after the expected measurement time had elapsed. Available at: http://www.correiodobrasil.com.br. Accessed on: May 2, 2010. On the date of the incident, two people saw the balloon. One was 1.8 km from the vertical position of the balloon and sighted it at an angle of 60º; the other was 5.5 km from the vertical position of the balloon, aligned with the first, and in the same direction, as seen in the figure, and sighted it at an angle of 30º. What was the approximate height of the balloon? a) 1.8 km b) 1.9 km c) 3.1 km d) 3.7 km e) 5.5 km 02. (ENEM-2011) To determine the distance of a boat to the beach, a navigator used the following procedure: from point A, he measured the visual angle α by aiming at a fixed point P on the beach. Keeping the boat in the same direction, he continued to point B so that it was possible to see the same point P on the beach, however at a visual angle 2α. The figure illustrates this situation: Suppose the navigator has measured the angle α = 30° and, upon reaching point B, found that the boat had traveled the distance AB = 2,000 m. Based on this data and maintaining the same trajectory, the shortest distance from the boat to the fixed point P will be a) 1,000 m. b) 1,000 √3 m. c) 2,000 √3/3 m. d) 2,000 m e) 2,000 √3 m. 03. (ENEM-2017) Rays of sunlight are hitting the surface of a lake forming an angle X with its surface, as shown in the figure. Under certain conditions, it can be assumed that the luminous intensity of these rays, on the surface of the lake, is given approximately by I(x) = k . sen(x) where k is a constant, and assuming that X is between 0° and 90°. When x = 30º, the light intensity is reduced to what percentage of its maximum value? a) 33% b) 50% c) 57% d) 70% e) 86% 04. (ENEM-2009) When he died, the father of João, Pedro and José left as an inheritance a rectangular plot of land measuring 3 km x 2 km that contains a gold extraction area delimited by a quarter of a circle with a radius of 1 km from the lower left corner of the property. Given the greater value of the gold extraction area, the brothers agreed to divide the property so that each would get a third of the extraction area, as shown in the figure. Regarding the proposed division, it can be seen that the percentage of the land area that went to João corresponds approximately to (consider ( √3)/3 = 0.58) a) 50%. b) 43% c) 37% d) 33% e) 19% 05. (ENEM-2018) To decorate a straight circular cylinder, a rectangular strip of transparent paper will be used, on which a diagonal is drawn in bold that forms 30° with the lower edge. The radius of the base of the cylinder measures 6/π cm, and by rolling the strip, a helix-shaped line is obtained, as in the figure. The value of the height of the cylinder, in centimeters, is a) 36√3 b) 24√3 c) 4√3 d) 36 e) 72 #enem #escoladenumeros