...generalizes the Pythagorean theorem is by showing that the square of a side of a triangle opposite an acute angle is less than the sum of the squares of the other two sides. What if we take the side of a triangle opposite an obtuse angle? Exercise Show that...

...Calculate to seven places' of decimals the logarithms of 2, 3, and 7 to the base 10, given M = -4342945. 1. In any triangle, the square of the side subtending...squares of the sides containing that angle, by twice the rectangle contained by either of these sides and the line intercepted between the perpendicular let...

...the squares of AD, BE, and CF, are together equal to three times the square of the hypothcnuse. (>. In any triangle the square of the side subtending an acute angle is less than the squares of the sides containing that angle by twice the rectangle contained by either of these sides,...

...produced to F, show that DH produced will cut BF at right angles. 8. In any triangle the square on the side subtending an acute angle is less than the sum of the squares on the sides containing the acute angle by twice the rectangle contained by one of these sides and...

...BCis less than the sum of the squares on AC,BC\ty the square on AB. 8. In any triangle the square on the side subtending an acute angle is less than the sum of the squares on the sides containing it by twice the rectangle contained by either of these sides and the portion...

...that, rf^g, then j where all the quantities are positive. 9. Prove that in every triangle the square on the side subtending an acute angle is less than the sum of the squares on the aides containing that angle by twice the rectangle contained by either of these sides, and the...

...under the whole and each of the parts. 3. The square of the side opposite an acute angle of a triangle is less than the sum of the squares of the sides containing it by twice the rectangle under either of them, and the segment of the other contained between the...