Sine (sin) = opposite hypotenuse
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1 ? Sine (sin) =?
2 Sine (sin) = opposite hypotenuse
3 ? Cosine (cos) =?
4 Cosine (cos) = adjacent hypotenuse
5 ? Tangent (tan) =?
6 Tangent (tan) = opposite adjacent
7 sin D=??
8 sin D = AB AD
9 cos D=??
10 cos D = DB AD
11 tan D=??
12 tan D = AB DB
13 B sin A=? 5 13? C 12 A
14 B 5 (opposite) C (hypotenuse) A sin A= 5 13 (opposite) (hypotenuse)
15 B sin B=? 5 13? C 12 A
16 B 5 13 (hypotenuse) C 12 (opposite) A sin B= (opposite) (hypotenuse)
17 B cos B=? 5 13? C 12 A
18 B 5 (adjacent) C (hypotenuse) A cos B= 5 (adjacent) 13 (hypotenuse)
19 B tan A=? 5 13? C 12 A
20 B 5 (opposite) C (adjacent) A tan A= 5 12 (opposite) (adjacent)
21 If the sin O = 3 for MON with 5 right M, what is the cos N?
22 N (opposite) 3 (adjacent) M If the sin O = 3 for MON with 5 right M, what is the cos N? (hypotenuse) O sin O = 3 5 = opposite hypotenuse 5 cos N = 3 5 = adjacent hypotenuse
23 If the cos A = for MAD with right M, what is the sin D?
24 A (opposite) 12 (adjacent) M If the cos A = for MAD with right M, what is the sin D? (hypotenuse) cos A = = adjacent hypotenuse 13 sin D = = opposite hypotenuse D
25 Which trigonometric expression has the same value as sin 48?
26 Which trigonometric expression has the same value as sin 48? cos 42
27 Which trigonometric expression has the same value as cos 52?
28 Which trigonometric expression has the same value as cos 52? sin 38
29 Use your calculator and round to the nearest ten thousandth. sin 48 =?
30 sin 48 =.7431
31 Use your calculator and round to the nearest hundredth. cos 79 =?
32 cos 79 =.1908
33 Use your calculator to find the measure of the angle to the nearest tenth degree. tan A= 4.64
34 tan A =
35 Use your calculator to find the measure of the angle to the nearest tenth degree. sin B=.5476
36 sin B=
37 53 x 40 Find the missing value. If not exact, round to the nearest hundredth.
38 53 x (hypotenuse) 40 (opposite) 40 sin 53 x x 50.09
39 x Find the missing value. If not exact, round to the nearest hundredth. 8.4
40 X (opposite) (adjacent) x tan x 18.46
41 20 x 76 Find the missing value. If not exact, round to the nearest hundredth. 8.4
42 x (hypotenuse) (adjacent) 20 cos76 x x 82.67
43 15 x 32 Find the missing value. If not exact, round to the nearest hundredth. 8.4
44 15 (opposite) 32 x (adjacent) 15 tan 32 x x 24.01
45 30 Find the missing value. If not exact, round to the nearest hundredth. 8.4
46 30 (hypotenuse) x sin x 11.24
47 x Find the missing value. If not exact, round to the nearest hundredth. 8.4
48 x Remember, you are finding an angle, therefor you use The key on your calculator sin 1 sin x x
49 x 17 8 Find the missing value. If not exact, round to the nearest hundredth. 8.4
50 x 8 (adjacent) 17 (opposite) Remember, you are finding an angle, therefor you use the key on your calculator tan 1 tan x x
51 14 18 x Find the missing value. If not exact, round to the nearest hundredth. 8.4
52 14 (adjacent) 18 (hypotenuse) x Remember, you are finding an angle, therefor you use the key on your calculator cos 1 cos x x
53 Johnny and Jeff are building a skateboard ramp that is 100 centimeters long and rises 75 centimeters. What is the angle of the ramp (m A)?
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55 Find the height of the building to the nearest foot. 63 x 85 ft
56 Find the height of the building to the nearest foot. 63 x 85 tan 63 = 85 a tan 63a tan 63 = 85 tan 63 a = 43 ft
57 William is an archaeologist completing field work in Egypt. William examines an ancient pyramid and determines that each side of the square base is 220 feet long. The angle of incline of each side of the pyramid is 50. How tall is the pyramid if the highest point is over the center of the base? Round your answer to the nearest whole foot.
58 William is an archaeologist completing field work in Egypt. William examines an ancient pyramid and determines that each side of the square base is 220 feet long. The angle of incline of each side of the pyramid is 50. How tall is the pyramid if the highest point is over the center of the base? Round your answer to the nearest whole foot. tan 50 = x 110 x = 110(tan50) x = 131 feet (opposite) x 110 (adjacent)
59 If the quarterback, Q, throws the football 45 yards from one 30-yard line to a player, P, located on the other 30-yard line, at what angle ( PQR), to the nearest degree, did the quarterback have to throw the football?
60 If the quarterback, Q, throws the football 135 feet from one 30-yard line to a player, P, located on the other 30-yard line, at what angle ( PQR), to the nearest degree, did the quarterback have to throw the football? cos x = x = cos 1 45 x = 27 (adjacent) 40 x 45 (hypotenuse)
61 An observer at the top of a 60 m lighthouse sights two ships approaching, one behind the other. The angles of elevation of the ships are 30 and 20. Find the distance between the ships to the nearest tenth.
62 An observer at the top of a 60 m lighthouse sights two ships approaching, one behind the other. The angles of elevation of the ships are 30 and 20. Find the distance between the ships to the nearest tenth. 60 m (opposite) x 30 (adjacent) tan 30 = 60 x tan 30x tan 30 = 60 tan 30 x = m 60 m (opposite) y 20 (adjacent) tan 20 = 60 y tan 20y tan 20 = 60 tan 20 y = m m m Final answer: =60.9 m
63 What variable represents the length of an adjacent leg for a 50 angle? c a 50 t
64 What variable represents the length of an adjacent leg for a 50 angle? t (hypotenuse) 50 c t (adjacent) a (opposite)
65 Find the measure of d, if o = 20. Round to the nearest whole. o d g 25
66 Find the measure of d, if o = 20. Round to the nearest whole. sin 25 = 20 d sin25 d sin 25 = 20 sin 25 d = o (opposite) g (hypotenuse) d 25
67 Find the measure of a, if t = 20. Round to the nearest whole. c a 50 t
68 Find the measure of a, if t = 20. Round to the nearest whole. tan 50 = a tan 50 = a 29 = a c 50 t 20 (adjacent) a (opposite)
14.1 Similar Triangles and the Tangent Ratio Per Date Trigonometric Ratios Investigate the relationship of the tangent ratio.
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