Ans: 30 units Solution: Since the sides of a right triangle satisfy the Pythagorean Theorem, a² + b² = c², we have 5² + 12² = 25 + 144 = 169 = 13². So, the three sides are 5, 12 and 13 and the perimeter is 5 + 12 + 13 = 30.

4. Why could a right triangle with integers for lengths of sides not have shorter sides measuring 5 and 10 units?

Solution: By the Pythagorean Theorem, 5² + 10² = 25 + 100 = 125 which is not a perfect square [125 ~ (11.1803...)²]. Thus, the third side cannot have an integer length.

6. Use the measurements of Eratosthenes to find the approximate difference in angle of elevation of the sun at two places 1000 km apart in a north-south direction, both north of the equator.

Solution: 787/7.2 = 1000/x, so x ~ 9.1º.

8. If the distance were 400 miles and the angle difference 8º, what would be the circumference of the planet?

Ans. 18,000 miles. Solution: If an angle of 8º corresponds to a distance of 400 miles, then 360º corresponds to (360/8)(400) = 18,000 miles.

10. Use the method of Figure 1.1b to estimate the radius of the earth if the airplane is flying at a height of 10 miles and the angle of depression is 4.01^o.

Ans: 4075 miles. Solution: In the figure, PC = 10 and angle BPC = 90^o - 4.01^o = 85.99^o. So, r/r+10 = sin 85.99^o, thus, r = 10 sin 85.99^o/ 1 - sin 85.99^o, so r is approximately 4075 miles.

12. Euclid used the word postulate for an assumption confined to one particular subject.

Ans: True.

14. Ethnomathematics is another name for cartography.

Ans: False. Solution: Ethnomathematics is the mathematics used on a regular basis by a group of people, while cartography is the science of making maps.