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Lesson 33 - Applications of Right Triangle Trigonometry IB Math SL1 – Santowski 7/21/2015 Math SL1 - Santowski 1 (A) Review of Right Triangles C HYPOTENUSE OPPOSITE SIDE ADJACENT SIDE Angle B A In a right triangle, the primary trigonometric ratios (which relate pairs of sides in a ratio to a given reference angle) are as follows: sine A = opposite side/hypotenuse side cosine A = adjacent side/hypotenuse side tangent A = opposite/adjacent side side recall SOHCAHTOA as a way of remembering the trig. ratio and its corresponding sides 7/21/2015 Math SL1 - Santowski 2 Examples – Right Triangle Trigonometry A support cable runs from the top of the telephone pole to a point on the ground 43 feet from its base. If the cable makes an angle of 32.98º with the ground, find (rounding to the nearest tenth of a foot): a. the height of the pole b. the length of the cable A POLE mABC = 32.98 B 7/21/2015 43 FEET Math SL1 - Santowski C 3 Examples – Right Triangle Trigonometry Mr Santowski stands on the top of his apartment building (as part of his super-hero duties, you know) and views a villain at a 29º angle of depression. If the building I stand upon is 200 m tall, how far is the villain from the foot of the building? 7/21/2015 A E ANGLE OF DEPRESSION = 29 BUILDING mADB = 29 C Math SL1 - Santowski B D 4 Examples – Right Triangle Trigonometry 7/21/2015 Math SL1 - Santowski 5 Examples – Right Triangle Trigonometry 7/21/2015 Math SL1 - Santowski 6 Examples – Right Triangle Trigonometry 7/21/2015 Math SL1 - Santowski 7 Examples – Right Triangle Trigonometry (6) Assuming that the Earth has a radius of 6380 km, determine the length of the 35th parallel. (7) To determine the width of a river, a surveyor marks a point on the bank of the river, A. Her partner is standing directly across the river from her at point C. The surveyor then walks 100 m downstream to point B, where she now has a line of sight to her partner at an angle of 58º relative to the river bank. Determine the width of the river. 7/21/2015 Math SL1 - Santowski 8 Examples – Right Triangle Trigonometry 7/21/2015 Math SL1 - Santowski 9 Examples – Right Triangle Trigonometry 7/21/2015 Math SL1 - Santowski 10 Examples – Right Triangle Trigonometry 7/21/2015 Math SL1 - Santowski 11 Examples – Right Triangle Trigonometry 7/21/2015 Math SL1 - Santowski 12 Examples – Right Triangle Trigonometry 7/21/2015 Math SL1 - Santowski 13 Examples – Right Triangle Trigonometry 7/21/2015 Math SL1 - Santowski 14 Examples – Right Triangle Trigonometry You are hiking along a river and see a tall tree on the opposite bank. You measure the angle of elevation of the top of the tree and find it to be 46.0º. You then walk 50 feet directly away from the tree and measure the angle of elevation. If the second measurement is 29º, how tall is the tree? Round your answer to the nearest foot. 7/21/2015 A TREE mABC = 46 C Math SL1 - Santowski mADB = 29 B D 15 Examples – Right Triangle Trigonometry (8) While driving towards a mountain, Mr S notices that the angle of elevation to the peak is 3.5º. He continues to drive to the mountain and 13 miles later, his second sighting of the mountain top is 9º. Determine the height of the mountain. 7/21/2015 Math SL1 - Santowski 16 Examples – Right Triangle Trigonometry 7/21/2015 Math SL1 - Santowski 17 Examples – Right Triangle Trigonometry 7/21/2015 Math SL1 - Santowski 18 Examples – Right Triangle Trigonometry 7/21/2015 Math SL1 - Santowski 19 (G) Homework 10CDEF - Right Angled Trig Review HW Ex 10C #1be, 2, 5, 6; Ex 10D #1ae, 3c, 4b, 5b, 6a, 7ac, 11,12; Ex 10E #2, 6, 8; Ex 10F #1bc, 2b,3a 7/21/2015 Math SL1 - Santowski 20