SaiBook.us SAT-2

Home Course Section

Schedule Admission Social

Lesson Example Discussion Quiz: Class Homework

Step-5

Title: Law of sines and cosines

Grade: 10-a Lesson: S3-L7

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Solve triangle ABC, given a = 15, b = 25, and c = 28. Find the angle A , B and C?
2	Step	The given value are	a = 15, b = 25, and c = 28
3	Formula:	The Law of Cosines states for CosA:	\$CosA = ((b)^2 + (c)^2 - (a)^2)/(2bc)\$
4	Step	Plug the values in the formula and then simplify for the value of CosA	\$CosA = ((25)^2 + (28)^2 - (15)^2) / (2 times 25 times 28)\$ \$CosA = (625 + 784 - 225) / (1(400))\$ \$CosA = 0.845\$ \$A = cos^-1 (0.845)\$ A = 32.3°
5	Formula:	The Law of Cosines states for CosB:	\$CosB = ((a)^2 + (c)^2 - (b)^2) / (2ac)\$
6	Step	Plug the values in the formula and then simplify for the value of CosB	\$CosB = ((15)^2 + (28)^2 - (25)^2) / (2 times 15 times 28)\$ \$CosB = (225 + 784 - 625) / (840)\$ \$CosB = 0.457\$ \$B = cos^-1(0.457)\$ B = 62.8°
7	Step	The sum angle in a triangle is 180°, so now find the value CosC	C = 180 - (A + B) C = 180 - ( 32.3 + 62.8) C = 84.9°
8	Step	So, the angles of triangle ABC are A = 32.3°, B = 62.8° and C = 84.9°.
9	Choice.A	Incorrect because the values for angles A and B are slightly off	A = 32°, B = 63° and C = 84.9°
10	Choice.B	Correct: It is accurately done the calculation by using the law of cosines formula	A = 32.3°, B = 62.8° and C = 84.9°
11	Choice.C	Wrong regarding angle C and B . The correct value should be approximately 84.7°, not 85° and angle B is 62.8 degree not 63 degrees	A = 32.3°, B = 63° and C = 85°
12	Choice.D	Option D is inaccurate as the calculated angle A and values for B and C differ from the provided data	A = 32.8°, B = 62.3° and C = 83.9°
13	Answer	Option	B
14	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Solve triangle ABC, given a = 15, b = 25, and c = 28. Find the angle A , B and C?

Step

The given value are

a = 15, b = 25, and c = 28

Formula:

The Law of Cosines states for CosA:

\$CosA = ((b)^2 + (c)^2 - (a)^2)/(2bc)\$

Step

Plug the values in the formula and then simplify for the value of CosA

\$CosA = ((25)^2 + (28)^2 - (15)^2) / (2 times 25 times 28)\$

\$CosA = (625 + 784 - 225) / (1(400))\$

\$CosA = 0.845\$

\$A = cos^-1 (0.845)\$

A = 32.3°

Formula:

The Law of Cosines states for CosB:

\$CosB = ((a)^2 + (c)^2 - (b)^2) / (2ac)\$

Step

Plug the values in the formula and then simplify for the value of CosB

\$CosB = ((15)^2 + (28)^2 - (25)^2) / (2 times 15 times 28)\$

\$CosB = (225 + 784 - 625) / (840)\$

\$CosB = 0.457\$

\$B = cos^-1(0.457)\$

B = 62.8°

Step

The sum angle in a triangle is 180°, so now find the value CosC

C = 180 - (A + B)

C = 180 - ( 32.3 + 62.8)

C = 84.9°

Step

So, the angles of triangle ABC are A = 32.3°, B = 62.8° and C = 84.9°.

Choice.A

Incorrect because the values for angles A and B are slightly off

A = 32°, B = 63° and C = 84.9°

Choice.B

Correct: It is accurately done the calculation by using the law of cosines formula

A = 32.3°, B = 62.8° and C = 84.9°

Choice.C

Wrong regarding angle C and B . The correct value should be approximately 84.7°, not 85° and angle B is 62.8 degree not 63 degrees

A = 32.3°, B = 63° and C = 85°

Choice.D

Option D is inaccurate as the calculated angle A and values for B and C differ from the provided data

A = 32.8°, B = 62.3° and C = 83.9°

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?