Law of Sines and Cosines Without Ambiguous Case

What is the distance across the river? The two sides are 4.15 miles and 5.33 miles. The included angle measure is 37 degrees.

• 2.9 miles

• 3.2 miles

• 3.6 miles

• 3.9 miles

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Identify the Law of Sines

• Sin²x + Cos²x =1

• Sin(A)/a = Sin(B)/b = Sin(C)/c

• Sin(A)Sin(B)Sin(C) = 1

• Soh-Cah-Toa

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Use the Law of Cosines to find the measure of angle x. The side lengths shown are 25, 32 and 37. <x is opposite the 25 length side.

• 38.5^o

• 41.7^o

• 45.1^o

• 51.3^o

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the length of side x? x is opposite a 28 degree angle. 14 cm is the side length given.

• 6.57 cm

• 7.05 cm

• 7.44 cm

• 8.33 cm

Tags

CCSS.HSG.SRT.C.8

Which Law would you use?

• Law of Sines

• Law of Cosines

• Law of the Jungle

• Law of Gravity

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Identify the Law of Sines

• Sin²x + Cos²x =1

• Sin(A)/a = Sin(B)/b = Sin(C)/c

• Sin(A)Sin(B)Sin(C) = 1

• y=Sin(x)

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

• A

• B

• C

• D

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55 degrees, and from Jamie to the bird is 63 degrees. How far away, to 2 decimal places, is the bird from Amanda?

• 25.23 ft

• 23.19 ft

• 22.15 ft

• 20.85 ft

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What is the area of this triangle to three decimal places?

• 14.494 meters squared

• 108.184 meters squared

• 54.092 meters squared

• 54.350 meters squared

Tags

CCSS.HSG.SRT.D.9

Find m<B to the nearest whole number.

• A

• B

• C

• D

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11