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Right Triangle Trigonometry Problem 1: • Mimi was walking on the school ground late in the afternoon. While walking, she was not looking on her steps. Suddenly, she stepped on a banana peel. • Luckily, Rekkah and Irene, her classmates were there to catch her from falling on the ground. • A scalene triangle was formed between her and Irene. A right angle was formed below Irene’s arms and an angle measuring 27o from Mimi’s armpit. Irene has a height of 1.45 m excluding her head. Find the length of Mimi’s body when she reached her slanting position. 27° 1.45 m x Solution: Let x be the hypotenuse Given the angle of 27° and an opposite side of 1.45 m. 27° 1.45 m x sinθ= opposite x sin27°= 1.45m X = 2.85 m substitute. x sin27°(x)= 1.45m sin 27° Sine theta is equal to opposite over hypotenuse. Multiply sin27° and hypotenuse. Final answer: x equals 2.85 m. Problem 2: It was past afternoon that time. Shayne and Rey was about to go home. Waving goodbye, Shayne, with a height of 1.78m, casted a shadow with an angle of elevation of 32 o. Find the length from Rey’s height if the overall length of their shadow is 6.49 m. Solution: let y be the length of the shadow of Shayne let x be the length of the height of Rey given 1.78m height of Shayne 32° angle of elevation 6.49 m total shadow casted Rey x Shayne 1.78m 32° 6.49 m y Tan θ= opposite adjacent Tan 32°= 1.78km Tan θ is equal to opposite over adjacent. substitute. x Tan 32°(x)= 1.78 km Tan 32° Tan 32° Cross multiply. divide tan 32° to the opposite side. answer: y = 2.85 km y equals 2.85 km Using proportion property: The height of the shadow casted by Rey is: Height = 6.49m – 2.85m = 3.64m x 1.78m = 3.64m 2.85m (2.85m) x = (1.78m)(3.64m) 2.85 m X = 2.27 m Final answer: the height of Rey is 2.27 m. Submitted by: Rey PJ Enerio Rekkah Niña Buliga Veronica Shayne Francisco Sheila Mae Gabe Irene Pilar Tecson