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

+1 vote
Use the Law of Cosines.  Find b to the nearest tenth. 
Triangle ABC with the measure of angle B = 48, the side opposite angle C = 85, and the side opposite angle “A” = 60.
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 triangle with one angle equal to 70 degrees.  The sides of that angle are 9 cm and 15 cm.
A. 126.9 cm2
B. 63.4 cm2
C. 23.1 cm2
D. 185.5 cm2
In triangle JKL, j = 9 inches, k = 5 inches and the measure of angle L = 43.  Find the measure of angle J.
A. 28º
B. 59º
C. 32º
D. 105º

 

asked Oct 7, 2014 in TRIGONOMETRY by tonymate Pupil

3 Answers

0 votes

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.

answered Oct 8, 2014 by david Expert
0 votes

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.

answered Oct 8, 2014 by david Expert
0 votes

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.

answered Oct 8, 2014 by david Expert

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