Download Chapter 12 Right Triangle Trigonometry

Chapter 12 Right Triangle Trigonometry
Review Notes:
What is the saying that helps us remember the Trig Functions: SOH-CAH-TOA
Which stand for:
sin(x  ) = Opp
Hyp
cos(x  ) = Adj
Hyp
tan(x  ) = Opp
Adj
If you look up from a horizontal, you measure the angle of elevation. If you look
down from a horizontal, you measure the angle of depression.
Illustrate the statement above:
Use your trigonometric table to find the value of:
*ROUND all answers to two decimal places
1) cos 23 = .92
2) tan 64 = 2.05
3) sin 52 = .79
4) tan 78 = 4.70
Use your trigonometric table to find the measurement of the angle whose:
5) cos A =0.94 m<A = 19.95°
6) sin B= 0.05 m<B = 2.87°
7) tan A =6.31 m<A = 80.99°
8) cos B= 0.69 m<B = 46.37°
9)
sin A = 6/10 = 3/5
A
10
8
C
6
4
cos A = 8/10 = 4/5
B
tan B = 8/6 = 4/3
Find x.
10)
11)
37
13
x
Cos(20) = 7/x
Sin(37) = 13/x
x = 7.45 yd.
X = 21.60
12)
13)
x
15
15
x
40
11 yd
Tan(40) = x/15
Cos(x) = 11/15
X = 12.59
X = 42.83°
14)
15)
Tan(x) = 8/14
B
24
Sin(x) = 14/24
x = 35.69°
14 yd
X = 29.74°
8
x
x
C
14 m
A
Complete each Question. Make sure you give a diagram, the equation and solution.
16) A tree casts a shadow of 30 meters when the angle of elevation to the sun is 20º. Find
the height of the tree to the nearest meter.
Diagram:
Equation:
Solution: 10.92 m
Tan(20°) = x/30
x
20°
30 m
17) The angle of elevation from a ship to the top of a 42m lighthouse on shore is 36
degrees. To the nearest meter, how far away is the ship from shore?
Diagram:
Equation:
Tan(36°) = 42/x
Solution: 57.81 m
42 m
36°
x
18) Kate is flying a kite. If the angle the string creates with the ground is 67 and
the kite is 35 ft in the air. To the nearest foot how much string has Kate let out?
Diagram:
35 ft
Equation:
Sin(67°) = 35/x
Solution: 38.02 ft.
x
67°
19) A 15-foot ladder is resting against a wall. If the base of the ladder is 5 feet
from the base of the wall, then what angle is the ladder making with the ground?
Diagram:
Equation:
Cos(x°) = 5/15
15 ft
x°
5 ft.
Solution: 70.53°