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Lesson Example Discussion Quiz: Class Homework

Step-1

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	In a given triangle PQR with P = 40° R = 104° and q = 12 then, solve for p.
2	Step	The given values are	P = 40°, R = 104° and q = 12
3	Hint	To solve for side p in triangle PQR, use the Law of Sines. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
4	Formula:	The low of sine is	\$ p / (sinP) = q / (sinQ) = r / (sinR)\$
5	Step	To use the Law of Sines, first find the angle Q	Q = 180 - (P + R) Q = 180 - (40 + 104) Q = 36°
6	Step	Plug the value in the formula and then simplify for value p	\$p / sin(40) = 12/sin(36)\$ \$p = (12 times sin(40)) / sin(36)\$ p = 13.1
7	Step	So, the length of side p is 13.1.
8	Choice.A	11.3, is inaccurate as it deviates from the calculated value	11.3
9	Choice.B	Option B is not correct because it suggests p = 12.1, which is not the correct value	12.1
10	Choice.C	Wrong: It provides a value of 14, which is not the correct solution to the problem	14
11	Choice.D	13.1 is accurately done the calculation by using the law of sines formula	13.1
12	Answer	Option	D
13	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

In a given triangle PQR with P = 40° R = 104° and q = 12 then, solve for p.

Step

The given values are

P = 40°, R = 104° and q = 12

Hint

To solve for side p in triangle PQR, use the Law of Sines. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Formula:

The low of sine is

\$ p / (sinP) = q / (sinQ) = r / (sinR)\$

Step

To use the Law of Sines, first find the angle Q

Q = 180 - (P + R)
Q = 180 - (40 + 104)
Q = 36°

Step

Plug the value in the formula and then simplify for value p

\$p / sin(40) = 12/sin(36)\$

\$p = (12 times sin(40)) / sin(36)\$

p = 13.1

Step

So, the length of side p is 13.1.

Choice.A

11.3, is inaccurate as it deviates from the calculated value

11.3

Choice.B

Option B is not correct because it suggests p = 12.1, which is not the correct value

12.1

Choice.C

Wrong: It provides a value of 14, which is not the correct solution to the problem

Choice.D

13.1 is accurately done the calculation by using the law of sines formula

13.1

Answer

Option

Sumup

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