Sine (sin) =

?

?

hypotenuse

oppositeSine (sin) =

Cosine (cos) =

?

?

hypotenuse

adjacentCosine (cos) =

Tangent (tan) =

?

?

adjacent

oppositeTangent (tan) =

sin D= ?

?

sin𝐷 =𝐴𝐵

𝐴𝐷

cos D= ?

?

cos𝐷 =𝐷𝐵

𝐴𝐷

tan D= ?

?

tan𝐷 =𝐴𝐵

𝐷𝐵

sin A=

C

B

A

5

12

13

?

?

sin A=

C

B

A

5

12

13

13

5

(opposite)

(hypotenuse)

(opposite)

(hypotenuse)

sin B=

C

B

A

5

12

13

?

?

sin B=

C

B

A

5

12

13

13

12

(hypotenuse)

(opposite)

(hypotenuse)

(opposite)

cos B=

C

B

A

5

12

13

?

?

cos B=

C

B

A

5

12

13

13

5 (adjacent)

(hypotenuse)

(adjacent)

(hypotenuse)

tan A=

C

B

A

5

12

13

?

?

tan A=

C

B

A

5

12

13

12

5

(adjacent)

(opposite)

(opposite)

(adjacent)

If the sin𝑂 =3

5for ∆𝑀𝑂𝑁 with

right ∠𝑀, what is the cos𝑁?

If the sin𝑂 =3

5for ∆𝑀𝑂𝑁 with

right ∠𝑀, what is the cos𝑁?

MO

N

sin𝑂 =3

5=

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒

ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒(hypotenuse)

3

(opposite)5 cos𝑁 =

3

5=

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒(adjacent)

If the cos 𝐴 =12

13for ∆𝑀𝐴𝐷 with

right ∠𝑀, what is the sin𝐷?

If the cos 𝐴 =12

13for ∆𝑀𝐴𝐷 with

right ∠𝑀, what is the sin𝐷?

cos 𝐴 =12

13=

𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡

ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

(hypotenuse)

12

(opposite)13 sin𝐷 =

12

13=

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒

ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒(adjacent)

MD

A

Which trigonometric expression has the same

value as sin 48°?

Which trigonometric expression has the same

value as sin 48°?

cos 42°

Which trigonometric expression has the same

value as cos 52°?

Which trigonometric expression has the same

value as cos 52°?

sin 38°

Use your calculator and round

to the nearest ten thousandth.

sin 48°= ?

sin 48°= .7431

Use your calculator and round

to the nearest hundredth.

cos 79°= ?

cos 79°= .1908

Use your calculator to find the

measure of the angle to the

nearest tenth degree.

tan A= 4.64

tan A = 4.64

77.8°

Use your calculator to find the

measure of the angle to the

nearest tenth degree.

sin B= .5476

sin B= .5476

33.2°

Find the missing value.

If not exact, round to the nearest

hundredth.

𝑥53°

40

𝑥 (hypotenuse)53°

40 (opposite)

50.09 x

x

4053sin

8.4

𝑥

40°

22

Find the missing value.

If not exact, round to the nearest

hundredth.

𝑋(opposite)

40°

22(adjacent)

18.46 x

22

x40tan

8.4

76°

20

𝑥

Find the missing value.

If not exact, round to the nearest

hundredth.

(adjacent)

(hypotenuse)

76°

20

𝑥

82.67 x

x

2076cos

8.4

15

32°

𝑥

Find the missing value.

If not exact, round to the nearest

hundredth.

15(opposite)

32°𝑥

(adjacent)

24.01 x

x

1532tan

8.4

30

Find the missing value.

If not exact, round to the nearest

hundredth.

30 (hypotenuse)

11.24 x

30

x22sin

8.4

Find the missing value.

If not exact, round to the nearest

hundredth.

𝑥° 37

12

18.92 x

37

12xsin

37

12

Remember, you are findingan angle, therefor you useThe key on your calculator

1sin

𝑥°

8.4

Find the missing value.

If not exact, round to the nearest

hundredth.

x

8

17

64.8 x

8

17xtan

Remember, you are findingan angle, therefor you usethe key on your calculator1tan

x

8

17(opposite)

(adjacent)

8.4

Find the missing value.

If not exact, round to the nearest

hundredth.

18

14

x

64.8 x

18

14xcos

Remember, you are findingan angle, therefor you usethe key on your calculator1cos

(hypotenuse)

(adjacent)

18

14

x

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)?

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)?(hypotenuse)

(opposite)sin 𝐴 =

75

100

𝐴 = sin−175

100𝐴 = 48.59°

Find the height of the building to the nearest foot.

63°

85 ft

x

Find the height of the building to the nearest foot.

63°

85

xtan 63 =

85

𝑎tan 63𝑎

tan 63=

85

tan 63𝑎 = 43 𝑓𝑡

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.

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.

(opposite)

(adjacent)110

x

tan 50 =𝑥

110𝑥 = 110(tan50)𝑥 = 131 feet

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?

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 =40

45

𝑥 = cos−140

45

𝑥 = 27°

(hypotenuse)

(adjacent)

45

𝑥°40

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.

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.

30°

60 m

𝑥

20°

60 m

𝑦

tan 30 =60

𝑥tan 30𝑥

tan 30=

60

tan 30𝑥 = 103.9 𝑚

(adjacent)

(adjacent)

(opposite)

(opposite)

tan 20 =60

𝑦tan 20𝑦

tan 20=

60

tan 20𝑦 = 164.8 𝑚

103.9 m

164.8 m

Final answer: 164.8-103.9=60.9 m

What variable represents the length of an adjacent leg

for a 50° angle?

50°

ca

t

What variable represents the length of an adjacent leg

for a 50° angle?

50°

ca

t

t

(adjacent)

(opposite)

(hypotenuse)

25°

do

g

Find the measure of d, if o = 20. Round to the nearest whole.

25°

do

g

Find the measure of d, if o = 20. Round to the nearest whole.

20

(opposite)

(hypotenuse)

sin 25 =20

𝑑𝑠𝑖𝑛25 𝑑

sin 25=

20

sin 25

𝑑 = 47

Find the measure of a, if t = 20. Round to the nearest whole.

50°

c

a

t

Find the measure of a, if t = 20. Round to the nearest whole.

50°

ca

t20

(adjacent)

(opposite)

tan 50 =𝑎

2020 tan 50 = 𝑎

29 = 𝑎