Lesson 26 - Review of Right Triangle Trigonometry PreCalculus Santowski PreCalculus - Santowski 1
(A) Review of Right Triangle Trig Trigonometry is the study and solution of Triangles. Solving a triangle means finding the value of each of its sides and angles. The following terminology and tactics will be important in the solving of triangles. Pythagorean Theorem (a 2 +b 2 =c 2 ). Only for right angle triangles Sine (sin), Cosecant (csc or 1/sin) Cosine (cos), Secant (sec or 1/cos) Tangent (tan), Cotangent (cot or 1/tan) Right/Oblique triangle PreCalculus - Santowski 2
(A) Review of Right Triangle Trig 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 & the cosecant A = csca = h/o cosine A = adjacent side/hypotenuse side & the secant A = seca = h/a tangent A = adjacent side/opposite side & the cotangent A = cota = a/o recall SOHCAHTOA as a way of remembering the trig. ratio and its corresponding sides PreCalculus - Santowski 3
(B) Review of Trig Ratios Evaluate and interpret: Evaluate and interpret: (a) sin(32 ) (b) cos(69 ) (c) tan(10 ) (d) csc(78 ) (e) sec(13 ) (f) cot(86 ) (a) sin(x) = 0.4598 (b) cos(x) = 0.7854 (c) tan(x) = 1.432 (d) csc(x) = 1.132 (e) sec(x) = 1.125 (f) cot(x) = 0.2768 PreCalculus - Santowski 4
(C) Review of Trig Ratios and Triangles PreCalculus - Santowski 5
(C) Review of Trig Ratios and Triangles PreCalculus - Santowski 6
(B) Examples Right Triangle Trigonometry Using the right triangle trig ratios, we can solve for unknown sides and angles: ex 1. Find a in ABC if b = 2.8, C = 90, and A = 35 ex 2. Find A in ABC if c = 4.5 and a = 3.5 and B = 90 ex 3. Solve ABC if b = 4, a = 1.5 and B = 90 PreCalculus - Santowski 7
(B) Review of Trig Ratios If sin(x) = 2/3, determine the values of cos(x) & tan(x) If cos(x) = 5/13, determine the value of sin(x) + tan(x) If tan(x) = 5/8, determine the sum of sin(x) + 2cos(x) If tan(x) = 5/9, determine the value of sin 2 (x) + cos 2 (x) A right triangle with angle α = 30 has an adjacent side X units long. Determine the lengths of the hypotenuse and side opposite α. PreCalculus - Santowski 8
Examples Right Triangle Trigonometry PreCalculus - Santowski 9
Examples Right Triangle Trigonometry PreCalculus - Santowski 10
(E) 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 PreCalculus - Santowski 11
(E) 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? PreCalculus - Santowski 12
(E) 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. PreCalculus - Santowski 13
Examples Right Triangle Trigonometry 2/18/14 Math SL1 - Santowski 14
Examples Right Triangle Trigonometry 2/18/14 Math SL1 - Santowski 15
Examples Right Triangle Trigonometry 2/18/14 Math SL1 - Santowski 16
Examples Right Triangle Trigonometry 2/18/14 Math SL1 - Santowski 17
Examples Right Triangle Trigonometry 2/18/14 Math SL1 - Santowski 18
Examples Right Triangle Trigonometry 2/18/14 Math SL1 - Santowski 19
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. 2/18/14 Math SL1 - Santowski 20
Examples Right Triangle Trigonometry 2/18/14 Math SL1 - Santowski 21
Examples Right Triangle Trigonometry 2/18/14 Math SL1 - Santowski 22