Lesson&3:&Determining&Angles&using&Trigonometry&& Unit&3& &Trigonometry&
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1 Lesson&3:&Determining&ngles&using&Trigonometry&& Unit&3& &Trigonometry& () Lesson)Context) BIGPICTUREofthisUNIT: CONTEXTofthisLESSON: ) HowdoIdeterminethemeasureofanglesingeometricshapes,withoutdirect measurement HowdoIsolveforsidesoranglesinrighttriangles HowdoImodelrealworldscenariosusingrighttriangles Wherewe vebeen Youknowhowtousetriangle trigtofindthemeasureofa sidegivenananglemeasure andasidelength. (B) Lesson)Objectives: a. Introducetheroleofaninverseinmathematics b. Determinethemeasureofanangleusingthetrigratios (C) Inverses)in)Mathematics a. Explainhowtosolvetheequationx+5=8 b. Explainhowtosolvetheequationx 5=8 c. Explainhowtosolvetheequation5x=8 d. Explainhowtosolvetheequation e. Explainhowtosolvetheequationx 2 =8 f. Explainhowtosolvetheequation g. OnethinghasbeenconstantinLLtheseexamples. Whereweare Howweuserighttriangle trigtofindthemeasure ofanangle h. Whatdoestheequationsin(x)=0.58meaninthefirstplace i. Sohowwouldwesolvetheequationsin(x)= Whereweareheading HowcanIsolveproblems thatinvolvinggeometric modelswithrighttriangles
2 Name: Skill Using Trigonometry to Solve for Missing Sides lgebra 1 Homework Date: In problems 1 through 3, determine the trigonometric ratio needed to solve for the missing side and then use this ratio to find the missing side. 1. In right triangle BC, m = 58 and B = 8. Find the length of each of the following. Round your answers to the nearest tenth. C (a) BC (b) C 58 8 B 2. In right triangle BC, m B = 44 and B = 15. Find the length of each of the following. Round your answers to the nearest tenth. (a) C B (b) BC C 3. In right triangle BC, m C = 32 and B = 24. Find the length of each of the following. Round your answers to the nearest tenth. B (a) C (b) BC C lgebra 1, Unit #8 Right Triangle Trigonometry L5 The rlington lgebra Project, LaGrangeville, NY 12540
3 Lesson&3:&Determining&ngles&Using&Trigonometry&& Unit&3& &Trigonometry& Opening ctivity: Use our DT TBLE of ratios & angles to help solve for the unknown angles ngle θ Opp/Hyp dj/hyp Opp/dj ngle θ Opp/Hyp dj/hyp Opp/dj θ=7 o θ=48 o θ=12 o θ=50 o θ=15 o θ=52 o θ=21 o θ=68 o θ=43 o θ=89 o θ=45 o Can you use your understanding of the above table to find the given angles How did you do it
4 -1- v D2h051h20 mkmuqt2ar ssbogflt3wrakr 5eN elglccd.e Z villk irmilgchvthsz mr7exsiexrovjemds.s y pmpadkej jwgihtqh4 uienzfwiwnh it8ez 9GEe0oJmPeItMrwyJ.W Worksheet by Kuta Software LLC Kuta Software - Infinite Geometry Name Inverse Trigonometric Ratios Find each angle measure to the nearest degree. 1) sin B = ) sin = Date Period 3) cos = ) cos W = ) cos = ) tan W = ) cos = ) tan W = Find the measure of the indicated angle to the nearest degree. 9) 10) ) 12) ) ) 27 11
5 pplications 4. n isosceles triangle has legs measuring 9 feet and a base of 12 feet. Find the measure of the base angle, x, to the nearest degree. (Remember: Right triangle trigonometry can only be used in right triangles.) 9 9 x skier is going down a slope that measures 7,500 feet long. By the end of the slope, the skier has dropped 2,200 vertical feet. To the nearest degree, what is the angle,, of the slope 7,500 feet 2,200 feet Reasoning 6. Could the following triangle exist with the given measurements Justify your answer lgebra 1, Unit #8 Right Triangle Trigonometry L6 The rlington lgebra Project, LaGrangeville, NY 12540
6 Math 2 3D Triangle Trigonometry
7 -1- P E20P1H29 ekoubtwaz csjolfztzwxaqrwet nlglfcq.s O J4lslW 1rliLg0hFt5sG Hr4epshe2rhvoeXdY.K n GMCaXdfeb Mw8ijtgh viun1fui8nbimtieq egqeowmne9tiroyg.g Worksheet by Kuta Software LLC Kuta Software - Infinite Geometry Multi-Step Trig. Problems Name Date Period Find the length of the side labeled x. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth. 1) 2) x x 3) 4) x x 44 Find the area of each triangle. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth. 5) 6)
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