 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Solutions for Session 8, Part C

See solutions for Problems: C1 | C2 | C3 | C4 | C5 | C6 | C7    Problem C1 The triangle with hypotenuse 4: By similarity with the original triangle, we can say: 5/4 = 3/a, so a = 12/5. The triangle with hypotenuse 10: By similarity with the original triangle, we can say: 5/10 = 3/a, so a = 30/5 = 6. The triangle with hypotenuse 1: By similarity with the original triangle, we can say: 5/1 = 3/a, so a = 3/5.   Problem C2 The triangle with hypotenuse 4: By similarity with the original triangle, we can say: 5/4 = 4/b, so b = 16/5. The triangle with hypotenuse 10: By similarity with the original triangle, we can say: 5/10 = 4/b, so b = 40/5 = 8. The triangle with hypotenuse 1: By similarity with the original triangle, we can say: 5/1 = 4/b, so b = 4/5.   Problem C3

 a. sin A = 3/5 and cos A = 4/5 b. sin B = 4/5 and cos B = 3/5   Problem C4

We calculate the hypotenuse with the Pythagorean theorem and find that it is 13.

 a. sin A = 12/13, cos A = 5/13 b. sin B = 5/13, cos B = 12/13 c. tan A = 12/5, tan B = 5/12   Problem C5

 a. sin 30° = cos 60° = 1/2 sin 60° = cos 30° = /2 tan 30° = 1/ tan 60° = These values are constant for any triangle with angles 30°-60°-90°. b. sin 45° = cos 45° = 1/ tan 45° = 1 These values are constant for any triangle with angles 45°-45°-90°.   Problem C6 Angles A and B are adjacent, so sin A = cos B. The hypotenuse is the same for both angles, but the roles of "adjacent side" and "opposite side" switch. The side opposite angle B is adjacent to angle A, and vice versa.   Problem C7 Let x be the length of the ramp. Then we have a right triangle with hypotenuse x, shorter leg 2, and the angle opposite to the shorter leg of 10°. Since sin 10° = 2/x, we have x = 2/sin 10° = 2/0.17 11.765 feet.     