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Lesson Example Discussion Quiz: Class Homework

Step-4

Title: Trigonometry ratios in right triangles

Grade: 1400-a Lesson: S3-L2

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

Lesson Steps

$4$

Step	Type	Explanation	Answer
1	Problem	In a right triangle ABC, right-angled at B, If tan A = 1 then find the value 2sinAcosA.
2	Step	The given value is	tan A = 1
3	Hint	If tan A = 1, it means that the length of the side opposite angle A is equal to the length of the adjacent side. Let’s denote this common length as x.
4	Formula:	Since it’s a right-angled triangle, the hypotenuse can be found using the Pythagorean theorem:	\$"Hypotenuse" = ("Opposite side")^2 + ("Adjacent side")^2\$
5	Step	In this case, it becomes:	\$"Hypotenuse"^2 = "x"^2 + "x"^2\$ \$"Hypotenuse" = (2"x")^2\$ \$"Hypotenuse" = "x"\sqrt(2)\$
6	Step	Now, substitute these values into 2sinAcosA	\$2"sinAcosA"= 2 times ("x" /("x" \sqrt(2))) times ("x" /("x"\sqrt(2)))\$
7	Step	Simplify this expression	\$2"sinAcosA" = 2(1/\sqrt2 times 1/\sqrt2)\$ \$2"sinA cosA" = 2/2\$
8	Step	Make it simpler	2sinA cosA = 1
9	Step	So, in this case, when tanA=1, the value of 2sinAcosA is 1.
10	Sumup	Can you summarize what you’ve understood in the above steps?
11	Choice.A	This option is incorrect because it suggests a value of 2, which doesn’t match the correct calculation of 1	2
12	Choice.B	This is the correct option as it correctly identifies the value of 2sin(A)cos(A) as 1 based on the given condition that tan(A) = 1	1
13	Choice.C	This option is incorrect because it suggests a value of -1, which doesn’t match the correct calculation of 1	-1
14	Choice.D	This option is incorrect because it suggests a value of -2, which doesn’t match the correct calculation of 1	-2
15	Answer	Option	B
16	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

In a right triangle ABC, right-angled at B, If tan A = 1 then find the value 2sinAcosA.

Step

The given value is

tan A = 1

Hint

If tan A = 1, it means that the length of the side opposite angle A is equal to the length of the adjacent side. Let’s denote this common length as x.

Formula:

Since it’s a right-angled triangle, the hypotenuse can be found using the Pythagorean theorem:

\$"Hypotenuse" = ("Opposite side")^2 + ("Adjacent side")^2\$

Step

In this case, it becomes:

\$"Hypotenuse"^2 = "x"^2 + "x"^2\$

\$"Hypotenuse" = (2"x")^2\$

\$"Hypotenuse" = "x"\sqrt(2)\$

Step

Now, substitute these values into 2sinAcosA

\$2"sinAcosA"= 2 times ("x" /("x" \sqrt(2))) times ("x" /("x"\sqrt(2)))\$

Step

Simplify this expression

\$2"sinAcosA" = 2(1/\sqrt2 times 1/\sqrt2)\$

\$2"sinA cosA" = 2/2\$

Step

Make it simpler

2sinA cosA = 1

Step

So, in this case, when tanA=1, the value of 2sinAcosA is 1.

Sumup

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

Choice.A

This option is incorrect because it suggests a value of 2, which doesn’t match the correct calculation of 1

Choice.B

This is the correct option as it correctly identifies the value of 2sin(A)cos(A) as 1 based on the given condition that tan(A) = 1

Choice.C

This option is incorrect because it suggests a value of -1, which doesn’t match the correct calculation of 1

-1

Choice.D

This option is incorrect because it suggests a value of -2, which doesn’t match the correct calculation of 1

-2

Answer

Option

Sumup

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