Question

Use the Law of Cosines.  Find b to the nearest tenth. 

	A.	102.2
	B.	62.4
	C.	132.9
	D.	63.2

Find the area of the triangle. Give the answer to the nearest tenth. The drawing may not be to scale. 

	A.	126.9 cm2
	B.	63.4 cm2
	C.	23.1 cm2
	D.	185.5 cm2

	A.	28º
	B.	59º
	C.	32º
	D.	105º

 

Answer 1

1) Observe diagram the triangle measurements are <B = 48°

And the sides are AB = c = 85 and

BC = a = 60

From cosine rule b²  = a²  + c²  - 2ac cosB

b²  = 60²  + 85²  - 2(60)(85) cos(48°)

b²  = 3600  + 7225  -10200 (0.6691)

b²  = 10825 - 6824.82

b²  = 4000.18

b = √4000.18

b = 63.24

b = 63.2

Option D is correct choice.

Answer 2

2) Let the traingle measurements are a = 9cm, b = 15cm and C = 70°

Calculate the area using Heron's formula

Area = 1/2 (ab) sinC

A = 1/2 (9)(15) sin(70)

A = 67.5 (0.9396)

A = 63.423

Area is 63.4 cm²

Option B is correct.

Answer 3

3)The measurements of the triangle are j = 9in, k = 5 in and <L = 43°

From cosine rule l²  = j² + k²  - 2jk cos(L)

l² = 9²  + 5²  - 2(9)(5) cos(43°)

l² = 81 + 25  - 90(0.7313)

l² = 106  - 65.817

l²  = 40.183

l = 6.339

From sine rule sin(K)/k = sin(L)/l

sin(K)/5 = sin(43°)/(6.339)

sin(K)/5 = 0.6819/6.339

sin(K)/5 = 0.1075

sin(K) = 5(0.1075)

sin(K) = 0.537

K = sin^-1(0.537)

K =   32.47

K = 32°

We know that the sum of the angles in a traingle = 180°

J = 180° - (43° + 32°)

J = 180° - 75°

J = 105°

<J = 105°

Option D is correct.