Download Ch. 7 Review

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Geometry Ch. 7 Review
1. Simply each expression.
a)√192
b)√98
c)√72
d)3√64+2√36
e)4√25+7√81
2. Find the geometric mean between each pair of numbers.
a) 3 and 24 b) 4 and 25 c) 6 and 9
d) 4 and 16 e) 8 and 12
3. Find the value of indicated side.
a) AC
b) AD, DC, and AC
4. Use the right triangle and the given
information to solve each problem.
a. Find BD and BC, if AD=8 and DC=23.
b. Find AB and BC, if AD=6 and AC=25.
c. Find AB and AC, if AD=2 and BD=3.
d. Find BC and AD, if AB=10 and AC=20.
5. Find the values of AB, AD, and BC; given BD=4 and DC=25.
6. Determine whether STU is a right triangle for the given vertices.
a. S(5,5), T(7,3), U(3,2)
b. S(-2,1), T(3,6), U(-4,-1)
c. S(-2,4), T(4,1), U(-1,-9)
7. Determine whether each set of measures can be the sides of a right triangle. Then state
whether they for a Pythagorean Triple.
a. 24, 32, 40
b. 7, 28, 29
c.2 2,2 7,6
9. A 6-meter ladder reaches higher up a wall when placed at a 70 angle then when placed at a
60 angle. How much higher, to the nearest tenth of a meter?
10. A guy wire is attached to the top of a 75-meter tower and meets the ground at a 65 angle.
How long is the wire?
11. A certain jet is capable of a steady 20 climb. How much altitude does the jet gain when it
moves 1 kilometer through the air? Answer to the nearest 50 meters.
12. Martha is 180 cm tall and her daughter Heidi is just 90 cm tall. Who casts the longer
shadow, Martha when the sun is 70 above the horizon, or Heidi when the sun is 35 above
the horizon? How much longer?
13. A road 1.6 km long rises 400 m. What is the angle of elevation of the road?
14. A kite is flying at an angle of elevation of about 40. All 80 m of string have been let out.
Ignoring the sag in the string, find the height of the kite to the nearest 10 m.
15. The bottom end of a ramp at a warehouse is 10 feet from the base of the main dock and is 11
feet long. How high is the dock?
16. Find the trigonometric ratio as a fraction and as a decimal rounded to four decimal places.
a. sin B
b. tan C
c. cos C
d. tan B
e. cos B
f. sin C
17. Find the value of x to the nearest tenth.
a.
b.
c.
18. Find y to the nearest degree.
a.
c.
d.
b.
d.
Answers
1a) 8√3
b) 7√2
c) 6√2
d) 36
e)83
2a) 6√2
b) 10
c) 3√6
d) 8
e) 4√6
3a )AC  161
b)AD  7,DC  13, AC  218
4a)BD  2 46,BC  713
b)AB  5 6,BC  5 19
c)AB  13,AC  6.5
d)BC 10 3,AD  5
5)BA  2 29, AD 10,BC  5 29
6a) No, ST  8,TU  17,US 13
b) No, ST  50,TU  98,US 8
c) Yes, ST  45,TU 125,US 170
7a) yes, yes
b) no, no
c) yes, no
9) 0.4 meter higher
10) wire=82.8’
11) altitude=350 m
12)Heidi, 63 cm
13)angle of elevation=14.5
14) height of kite=50 m
15)x  21  4.6
12
10
16a)sin B 
 .8
b)tan C 
 .8333
15
12
12
10
d)tan B 
 1.2
e)cos B 
 .6667
10
15
17a)x  20.0
b)x  23.3
c)x  32.6
18a)y  34
b)y  67
c)y  31
12
 .8
15
10
f )sin C 
 .6667
15
d)x  90.2
d)y  38
c)cos C 