# A use dynamic geometry software to construct a right

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a.Use dynamic geometry software to construct a right triangle with acute anglemeasures of 30°and 60°(a 30°- 60°- 90°triangle), where the shorter leg lengthis 3 units.b.Find the exact ratiosof the side lengths(using square roots).ABAC=0321451043215ACBABBC=ACBC=c.Repeat parts (a) and (b) for several other 30°- 60°- 90°triangles. Use your resultsto write a conjecture about the ratios of the side lengths of a 30°- 60°- 90°triangle.Communicate Your AnswerCommunicate Your Answer3.What is the relationship among the side lengths of 45°- 45°- 90°triangles?30°- 60°- 90°triangles?USING PRECISEMATHEMATICALLANGUAGETo be proficient in math,you need to expressnumerical answers witha degree of precisionappropriate for theproblem context.SamplePointsA(0, 4)B(4, 0)C(0, 0)SegmentsAB=5.66BC=4AC=4AnglesmA=45°mB=45°SamplePointsA(0, 5.20)B(3, 0)C(0, 0)SegmentsAB=6BC=3AC=5.20AnglesmA=30°mB=60°G.9.BTEXASESSENTIALKNOWLEDGEANDSKILLS
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Chapter A / Exercise 32
Precalculus: Mathematics for Calculus
Redlin/Stewart
Expert Verified
9.2LessonWhat You Will LearnWhat You Will LearnFind side lengths in special right triangles.Solve real-life problems involving special right triangles.Finding Side Lengths in Special Right TrianglesA 45°- 45°- 90°triangle is anisosceles right trianglethat can be formed by cutting asquare in half diagonally.Finding Side Lengths in 45°- 45°- 90°TrianglesFind the value ofx. Write your answer in simplest form.a.x845°b.xx52SOLUTION2.REMEMBERA radical with index 2is in simplest form whenno radicands have perfectsquares as factors otherthan 1, no radicandscontain fractions, andno radicals appear in thedenominator of a fraction.Previousisosceles triangleCore VocabularyCore VocabularyTheoremTheoremTheorem 9.445°- 45°- 90°Triangle TheoremIn a 45°- 45°- 90°triangle, the hypotenuse is2 times as long as each leg.ProofEx. 19, p. 480hypotenuse=leg2xxx245°45°
b.By the Base Angles Theorem (Theorem 5.6) and the Corollary to the Triangle SumTheorem (Corollary 5.1), the triangle is a 45°- 45°- 90°triangle.
476Chapter 9Right Triangles and Trigonometry
Section 9.2Special Right Triangles477Finding Side Lengths in a 30°- 60°- 90°TriangleFind the values ofxandy. Write your answerin simplest form.SOLUTIONStep 1Find the value ofx.

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Term
Fall
Professor
Michael McCall
Tags
Right triangle, triangle, Triangle Theorem
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Chapter A / Exercise 32
Precalculus: Mathematics for Calculus
Redlin/Stewart
Expert Verified