Plane and solid geometry . X D Fig. Given A^^X, with zlx acute j and p, the projection of bupon a. To find the value of o^ in terms of a, b, and p. Argument 1. In rt. A BAD, or = 11)^ + Db^. 2. But AD^ = b^-p\ 3. And DB = a—p (Pig. 1) or p —a (Fig. 2). 4. .-. DB = a- — 2ap+ p^, 5. .-. x = b--2r + « -2ap + p-, a:^ = a^+ b-— 2 ap. 453. Question. Why is it not necessary to include here the figureand discussion for a right triangle ? Reasons 1. §446. 2. §447. 3. § 54, 11. 4. § 54, 13. 5. §309. 198 PLANE GEOMETRY 454. Prop. XXVIII may be stated in the form of atheorem as follows: In
Plane and solid geometry . X D Fig. Given A^^X, with zlx acute j and p, the projection of bupon a. To find the value of o^ in terms of a, b, and p. Argument 1. In rt. A BAD, or = 11)^ + Db^. 2. But AD^ = b^-p\ 3. And DB = a—p (Pig. 1) or p —a (Fig. 2). 4. .-. DB = a- — 2ap+ p^, 5. .-. x = b--2r + « -2ap + p-, a:^ = a^+ b-— 2 ap. 453. Question. Why is it not necessary to include here the figureand discussion for a right triangle ? Reasons 1. §446. 2. §447. 3. § 54, 11. 4. § 54, 13. 5. §309. 198 PLANE GEOMETRY 454. Prop. XXVIII may be stated in the form of atheorem as follows: In any triangle, the square of the side opposite an acute angleis equal to the sum of the squares of the other two sides dimin-ished by twice the loroduct of one of these sides and the projec-tion of the other side upon it. Ex. 726. If the sides of a triangle are 7, 8, and 10, is the angleopposite 10 obtuse, right, or acute ? Why ? Ex. 727. Apply the statement of Prop. XXVIII to the square of anarm of a right triangle. Ex. 7
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
