Basic Mathematics for College Students

Chapter 9 Summary and Review 821

REVIEW EXERCISES

Refer to the right triangle below.

39. Find , if cm and cm.


40. Find , if ft and ft.


41. Find , if in. and in.


42. Find , if b a 21 ft and c 29 ft.

a b 77 c 85

c a 8 b 15

c a 5 b 12

a

c

b 46. TV SCREENS Find the height of the television

screen shown. Give the exact answer and an

approximation to the nearest inch.

Determine whether each triangle shown here is a right triangle.

47. 
    
    
    
    48. 9
    
    
    
    

7

2

8

11

15

52 in.

41 in.

48 in.

55 in.

Support cable

The converse of the Pythagorean theorem:
If a triangle has sides of lengths , , and , such that
a^2 b^2 c^2 , then the triangle is a right triangle.

ab c

Is the triangle shown here a right triangle?

We must substitute the longest side length,

12, for , because it is the possible

hypotenuse. The lengths of 8 and 10 may be

substituted for either or.

This is the Pythagorean equation.

Substitute 8 for a,10 for b,and 12 for c.

Evaluate each exponential expression.

This is a false statement.

Since 164  144 , the triangle is not a right triangle.

164  144

64  100  144

82  102  122

a^2 b^2 c^2

a b

c

12 cm

10 cm

8 cm

The lengths of two sides of a right triangle are given. Find the
missing side length. Give the exact answer and an approximation
to the nearest hundredth.

45. HIGH-ROPES ADVENTURE COURSES A

builder of a high-ropes adventure course wants to

secure a pole by attaching a support cable from

the anchor stake 55 inches from the pole’s base to a

point 48 inches up the pole. See the illustration in the

next column. How long should the cable be?

30 in.

20 in.

16 m 5 m