9.1 – 9.3 Solving Right Triangles without Trigonometry

2. Find the length of the altitude drawn to the hypotenuse.

158

x

a) x = 10.95

b) x = 11.5

c) x = 13.56

d) None of the above

<Explanation follows.>

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2. Solution

158

x You can redraw the triangles:

B

A

C D

C

BD

A

C8

x

x

1523

15

x

x

8

So,

x2 = 8*15

x2 = 120

x = 10.95 (A)

3. Find the value of x.

194

x

a) x = 219

b) x = 437

c) x = 223

d) x = 23

<Explanation follows.>

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3. Solution

You can redraw the triangles:

B

A

C D

C

BD

A

C4

xx 1923

23

x

x

19

So,

x2 = 19*23

x2 = 437

x = 437

194

x

19

4. The geometric mean of 5 and 15 is:

a) 3

b) 10

c) 5 3d) 75

<Explanation follows.>

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4. Solution

Geometric mean:

15

x

x

5

So,

x2 = 75

x = 75

x = 253

x = 53

9. Find the value of x.

a) 8.3

b) 7.0

c) 10.1

d) 1.9

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10. Choose the sets that are possible side lengths of a right triangle.

a) 1,1,2

b) 1,1,2c) 3,4,7

d) 3,4,5

e) a and c

f) b and d

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10.A. Find the side length of a square with a diagonal of length 10.

10

a) 3

b) 4.5

c) 7.07

d) 9

<Explanation follows.>

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10.A. Solution

So,

x2 + x2 = 100

2x2 = 100

x2 = 50

x = 7.07

10x

x

15. Find the value of h.

10

6h

11.6

a) h = 3.5

b) h = 5.1

c) h = 7.5

d) h = 10.77

<Explanation follows.>

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15. Solution

You can redraw the triangles:

B

A

C D

C

BD

A

C

h1010

h

11.6

h

10

6

11.6

10

6h

11.6

6

6

h

6

10

11.6

11. Which statements are true about options B and C in #11?

a) B is acute and C is obtuse

b) B is obtuse and C is acute

c) B is acute and C is not a triangle

d) B is obtuse and C is not a triangle

<Explanation follows.>

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11. SolutionB.6,7,12

C.20.8, 39, 74.2

Put the largest first and confirm it can be a triangle.

If yes, square them and compare largest to other two:

B. 122 _____ 62 + 72

144______ 36 + 49

C. 74.2______20.8 + 39

13. Find the value of x.

127

x

a) x = 257

b) x = 133

c) x = 19

d) x = 221

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