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Geometry Session 8: Solutions
 
Session 8 Part A Part B Part C Homework
 
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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.

<< back to Problem C1


 

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.

<< back to Problem C2


 

Problem C3

a. 

sin A = 3/5 and cos A = 4/5

b. 

sin B = 4/5 and cos B = 3/5

<< back to Problem C3


 

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

<< back to Problem C4


 

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°.

<< back to Problem C5


 

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.

<< back to Problem C6


 

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.

<< back to Problem C7


 

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