Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
MCR3U Sec. 5.1 Trigonometric Ratios of Acute Angles Review of Skills from Grade 10 A) Pythagorean Theorem for Right Triangles Only hypotenuse (hypotenuse)2 = sum of the squares of the other two sides Example # 1: Find the length of the missing side. 15 m a) b) y x 12 cm 25 m 5 cm B) Primary Trigonometric Ratios for Right Triangles Only hypotenuse hypotenuse opposite adjacent adjacent opposite The three primary trigonometric ratios are sine (sin), cosine (cos) and tangent (tan). The acronym we use to help us remember the relationship between the sides of the right triangle and the angle is "SOH CAH TOA" 1 MCR3U Example # 2: State the primary triognometric ratios for angle D. 8 mm adjacent 8 mm 17 mm 17 mm opposite hypotenuse Reciprocal Trigonometric Ratios Just like there are 3 primary trigonometric ratios, there is also 3 reciprocal trigonometric ratios. They are cosecant (csc), secant (sec) and cotangent (cot). Example # 3: Evaluating the six trigonometric ratios of an angle. Triangle XYZ is a right triangle with side lengths of 10 cm , 24 cm and 26 cm. If YZ = 10 cm and angle Z is 900, which trigonometric ratio of angle Y is the greatest? Example # 4: Solving for a side or angle in a right triangle. a) John is lying on the ground, 3.7 m b) from the base of a tree. He measures the angle of inclination to the top of the tree to be 650 using a clinometer. How tall is the tree, to the nearest tenth of a meter? A wheelchair ramp rises 8" for every 1 foot of horizontal distance. A wheel chair ramp into a new house needs to be built. The door is 4 feet above ground level. What angle of elevation should the ramp be constructed at to maintain the proper proportions? Therefore the height of the tree is approximately 7.9 m tall. Therefore the ramp should be constructed with an angle of elevation of 33.7o Homework p. 280 # 1-4 , 5ab (i,iii) , 6ac , 7a , 8b , 11 , 12 2