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GEOMETRY
Review for Test on Trigonometry
Show all work.
12
B
t?-
35
l. sinA= 37
2.
g
tanC= lZ
cosQ=
tanR=
.5
3. llslnx=-.thencosx=
8
tanx=
ø
8
-_lF.'
zL7
t7
z
x
-,t31
5'+ nL = E?
4z= (t¿l-25
o'=
X
a.=
31
la
Solve for each variable.
cos3l=+
\=
þMst= *
tS(<"s st)
{=
-S-
ôrrSl
x
4. x = \7.bG
5. x= c. qB
24
tz,rt
¿t,
=
#
X = z1 (t"" zc)
rectangle
6. x= G+Lt'l
G+"
x= \\3(
-L2t
X
cos 35=
sìn
Sin lo'l
tL (sinto<)
tL
T
y = tz(cos
zs)
3ìn 2'l
$.t.8S
sìn 3l
g. * =
\2.45
X
S,¡ t{f,
swbr
W
9^^
{=
10.
\b,q t{
i,
b5
=
g++¿=
= t=b
.L
ll. x= ZO'ft
ts
12. ABCD is a rhombus
AB =
AC
18
=
BD =
lr,.,a Q.r )L
(7
nZ.ABC = 78
L2-,
bb
Cos 5q =jh
t!
2l,qS
13.
*= !,tO
y=
Y.:
\trLãvrÍ¡t
,(a*.-3ÂlI
Sv-.G
t
È¡nGt
\\,
2Ø
*
14.
The equal sides of an isosceles triangle are l6 inches. If each base angle is 32 degrees,find
the length of the altitude.
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15. A tree casts a 4O-foot shadow at a time when the measure of the angle of elevation
of the
ind the height of the tree.
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16.
an angle of depression of 10 degrees. How far is the fire from a point directly underneath
the tower and on the same level as the surrounding ground?
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17. At a point on the ground 80 feet from the base of a building, the measure of the angle of
elevation to the top of the building is 5l degrees. Find the height of the building.
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+a^b\o
=#
qg.?q
s
6-u
18. Find the measures of the acute angles
of a 3-4-5
30 degrees and 60 degrees.)
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3G,??
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19. A rhombus
è¡n.5=+ 3o".-'(Ð =l
has a 12 cm side and a76 degree angle. Find the
b
tz
sh^36 -X
\z
20. A road climbs at a 5o angle. What is the grade of the road?
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Æ
lsò
2L
You are flying a kite and have let out 80 meters of string. The kite's angle of elevation
with the ground is 40 degrees. If the string is stretched straight, how high is the kite above
the ground?
Sr",. Hb =X
rÒ
I
rx
22.
bt,¿l
zs+
Use what you know about a 30-60-90 triangle to find the exact value for tan 30o.
lc.^ bo'
ôc-
\3
23. A helicopter is hovering over a landing pad 100 meters from you are standing. The
helicopter's angle of elevation with th round is l2 degrees. What is the altitude of the
helicopter?
S'rn r2"
6l-
?--
24.
x
\oÒ
=-
_x
tþ'^ lZ 'tú
An airplane climbs at an angle of 18 degrees with the ground. Find the ground distance
plane travels as it moves 2500 meters through the air.
K
CoS 18 =.7sø
25.
You are driving toward a mountain. At a rest stop you use a clinometer (a pocket device
that can measure the angle of elevation) to measure the angle of inclination from your eye
to the top of the mountain. The angle measures 11.5o. You then drive toward the mountain
on level ground for 5 miles. You stop and measure the angle of inclinati on to 27 .5". Find
the height of the mountain.
\tr'
-/
x
srh ll.f
Y
3, bL
slrl zt.ç = *,,
26. Giventhe following triangle. Explain why
Sl4
=
tiT u
{<4<{<TEST
€-aD
QUESTION:F*d<
sf'n
t/+
=
I
3in $= [
1,,
[a
= sUrt. b
:
sdn3'<
T-tavrsì'|ru. ?r"1..rtY
oBÇffi P'gt
.r, = sòA 8Ó.oa',
27. o=
a lô.51
qL
28.
a-L= 1.1 - + t2.32- z&.lxlz.B)<rs16
n- -- ll 7'll o l sqt
mzA= 9tl . 7O'
o- = lO.
g\
a
mZB =
mZ.C= lO.Llî'
s¡n
5't.1
ì
Q e â;t
_ úz
te
/E- fq
:Æ:--
(2@i)
.sz7--cc,sA
,
-z(z)(to). cntA
8( - 1- roo -- - zþ)(to\'eosA
1' =
zz +
lôz
tf-4-fg =cosA
--eosÛ
md
-Lto
-Æ.=
29, Two airplanes leave an airport, and the angle between
their flight paths is 40o. An hour
later, one plane has traveled 300 miles while the other has traveled 200 miles. How far
apart are the planes at this time?
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