Geometry: An Interactive Journey to Mastery

F௘ͽ 33° 15° 12 ab Figure 17.10  G௘ͽ 65° 41° 32 a b Figure 17.11 At 6 p.m., the Sun has an angle of elevation of 10.6°. At th ...

Lesson 17: Trigonometry through Right Triangles Compute the value of the length wͼ௘6HHFigure 17.13௘ͽ 7KHDQJOHRIGHSUHVVLR ...

What Is the Sine of 1°? Lesson 18 Topics x The sine and cosine addition formulas. x The “error term” in the Pythagorean theore ...

Lesson 18: What Is the Sine of 1°? Example 1 A calculator gives sin 1° |0.017. What, then, is sin 2° and sin 3°? Solution 7KHRE ...

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Lesson 18: What Is the Sine of 1°? Show that tan 2 x (^) 1tan2tan 2 xx. Show that tan xy 1tantantan xyxytan. Consider ...

The Geometry of a Circle Lesson 19 Topics x Notation and jargon. x The converse of Thales’s theorem. x The tangent/radius the ...

Lesson 19: The Geometry of a Circle 5HVXOWV x radius/tangent theorem:  7KHDQJOHEHWZHHQDUDGLXVDQGDWDQJHQWWRDFLUFOHͼ௘ ...

([DPSOH In )LJXUH, O is the center of the circle. Given: PS is the diameter. OQ SR&. Prove: Arcs PQ and QR are congru ...

Lesson 19: The Geometry of a Circle ([DPSOH 6\GQH\$XVWUDOLDKDVODWLWXGHƒVRXWKͼ௘6HH)LJXUH௘ͽ The radius of the ...

3LWIDOO x Drawing in the radii to the endpoints of an arc marked with an angle measure can make a picture overly complicated. D ...

Lesson 19: The Geometry of a Circle  Tangent circles with centers A and B have radii of 8 and 6, respectively. Find the lengt ...

The Equation of a Circle Lesson 20 Topics x The equation of a circle. x Pythagorean triples. )RUPXOD x The equation of a circ ...

Lesson 20: The Equation of a Circle ([DPSOH Explain why the circle xy (^132) ©¹ ̈ ̧§· 2125242 must be tangent to the x-axis ...

J௘ͽ xxyy^22  288. K௘ͽ xxyy^22  20 10 25 0.  Write the equation of a circle with the following information. D௘ͽ & ...

Lesson 20: The Equation of a Circle  )LQGWKHHTXDWLRQRIWKHFLUFOHZLWKFHQWHUͼ௘í௘ͽWDQJHQWWRWKHy-axis.  Conside ...

 6KHLODFODLPVWKDWWKHWZRFLUFOHVJLYHQE\ͼ௘x௘ͽ^2 ͼ௘yí௘ͽ^2 = 49 and x^2 + y^2 – 6x + 16y + 37 = 0 are H[WHUQDOO\ ...

Lesson 21: Understanding Area Understanding Area Lesson 21 Topics x The area congruence and area addition postulates. x The ar ...

([DPSOH A trapezoid has bases of length a and b and height h, as shown in )LJXUH. Find a formula for its area. 6ROXWLRQ D ...

Lesson 21: Understanding Area 3LWIDOO x You can memorize that the area of a parallelogram is “base times height” or that the ar ...