Download REVIEW Chapter 8: Trigonometric Ratios 8.1 Geometric Mean

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Per.
REVIEW Chapter 8: Trigonometric Ratios
8.1 Geometric Mean
1. Write a similarity statement comparing the three
triangles in the diagram.
2. Find x, y, and z.
z= J r i ^
z
7 3
n
, 2
^
if
x=
y=
5
7=
3. The Coast Guard has sent a rescue helicopter to retrieve passengers off a disabled ship.
The ship has called in its position as 1.7 miles from shore. When the helicopter passes over
a buoy that is known to be 1.3 miles from shore, the angle formed by the shore, the
helicopter, and the disabled ship is 90°. Determine what t h ^ ^ i m e t e f w o u l d read to the
nearest foot when the helicopter is directly above the buoy. ^ ^ 5 , ^ ^ ^ ^ aJhti^^^-c^
52^6
'
'>^^
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Date
8.2 Trigonometric Ratios
(Check that your calculator is in DEGREE mode. Tip: If tan45=l, then your calculator is in the correct mode.)
4. Trig Ratios: Soh-Cah-Toh
s i n Z A : lf£i£l_
cosZA=''f^
t a n Z A = ^ ^
5. Given the triangle below, find the sin, cos, and tan for angle M and T. As a fraction and decimal
to the hundredths place.
i—,
R
cos
tin Z M = 1
^ «-71
tail
6. If 0 = 14 ° and the hypotenuse is 12, what is the approximate perimeter of the triangle?
a.)
14.5
26.5
c. )
2.9
d. )
U.6
^'
^
1-2.
______
opp
I -i,
a^.--'=f''^'''^
7. If c = 50 and angle X is 65 degrees, what is the approximate area of the triangle?
a. )
b. )
do:
352.23
402.45
423.22
478.77
ft.^ b i t
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Date
Name
8. A right triangle has an angle that measures 55°. The leg adjacent to this angle has a length of 43
cm. What is the length of the other leg of the triangle? Round to the nearest tenth.
-•an
6S -
-q^
9. Right triangle ABC is gfaphed on the coordinate plane and has vertices at A ( - l , 3), li(0, 5), and
C(4, 3). What is the measure of Z C to the nearest^egre£2
8.3 Inverse of Trig. Ratios
10. Using trig ratios, Solve the right triangles. Round angles to the nearest degree and sides to
the hundredths.
a.
/O
CDS P S
C0S3S
d.
11. A ramp was built by the loading dock. The height of the loading platform is 4 feet. Determine
the length of the ramp if it makes a 32° angle with the ground.
12. Janelle sets her treadmill grade to 6%. What is the angle that the treadmill surface makes with a
horizontal line? Round to the nearest degree. A,^^ 13. If cos A= 0.28, which angle in the triangles below is Z A ?
^ ^ ^ ^ ^ ^
9 cm
40 cm
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Date
Per.
8.4 Angle of Elevation and Depression
14. A jet rises vertically 2000 feet over a horizontal distance of 2856 feet. To the nearest degree,
what is the angle of elevation of the jet's path?
15. Mayuko is sitting 30 feet high in a football stadium. The angle of depression to the center of the
field is 14°. What is the horizontal distance between Mayuko and the center of the field? Round
to the nearest foot.
I -^JH'
-u«.^izj*_ 5 o
So
4^nlM
16. A surveyor 50 meters from th^asejof a cliff measures the angle of elevation to the top of the
cliff as 72°. What is the height of the cliff? Round to the nearest meter.
X ^ So
•^K>7P
4
yy-Or^hji.
17. The figure shows a person parasailing. What is x, the height of the parasailer, to the nearest
foot?
3L? -
>
18. Shane is 61 feet high on a ride at an amusement park. The angle of depression to the park
entrance is 42°, and the angle of depression to his friends standing below is 80°. How far from
the entrance are his friends standing? Round to the nearest foot.
19. Solve the following quadratic equations.
a. 6 - 2 x 2 = -194
x - O
'
b. - 5 + 4x2 = 11
20. Simplify the radicals
a.
VT25
b. VT92
-
5vr^
r gvTl
;i ^
-7.
4-4
j
SmCi
i t
5
t
4-
r—r
J
r
-4-
;—r-