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Lesson Example Discussion Quiz: Class Homework

Step-5

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

$5$

Step	Type	Explanation	Answer
1	Problem	In a triangle XYZ, right-angled at Y, XY = 15 inches, and angle \$ X = 30^o\$. Find cos X.
2	Step	The given values are	XY = 15 inches, \$ X = 30^o\$
3	Step	To find the cosine of angle X in the right triangle XYZ, you can use the definition of cosine, which is the ratio of the adjacent side to the hypotenuse.
4	Step	Find the length of side XZ (the hypotenuse) using trigonometric ratios in a right triangle. Using the sine function, we have:	\$ "cos"("X") = ("Adjacent") / ("Hypotenuse") \$ \$sin(30^o) = "XY"/"XZ"\$ \$1/2 = 15 / "XZ"\$
5	Step	Cross multiply:	\$XZ = 15/(1/2)\$ \$XZ = 15 times 2\$ XZ = 30 inches
6	Step	Now, calculate cosine X:	\$cos(X) = "XY" / "XZ"\$ \$cos(X) = 1/2\$
7	Step	So, the cosine of angle X is \$1/2\$.
8	Choice.A	Correct representation using the cosine formula	\$1/2\$
9	Choice.B	The cosine function only outputs values between -1 and 1. Therefore, -2 is not a possible value for the cosine function so wrong	-2
10	Choice.C	This is incorrect. It states \$−1/2\$, which is the cosine of 60 degrees, not 30 degrees	\$-1/2\$
11	Choice.D	The cosine of an angle cannot be greater than 1 or less than -1 because the cosine function’s range is between -1 and 1 so wrong	2
12	Answer	Option	A
13	Sumup	Can you briefly tell me what you’ve learned and understood in today’s lesson?

Step

Type

Explanation

Answer

Problem

In a triangle XYZ, right-angled at Y, XY = 15 inches, and angle \$ X = 30^o\$. Find cos X.

Step

The given values are

XY = 15 inches, \$ X = 30^o\$

Step

To find the cosine of angle X in the right triangle XYZ, you can use the definition of cosine, which is the ratio of the adjacent side to the hypotenuse.

Step

Find the length of side XZ (the hypotenuse) using trigonometric ratios in a right triangle. Using the sine function, we have:

\$ "cos"("X") = ("Adjacent") / ("Hypotenuse") \$

\$sin(30^o) = "XY"/"XZ"\$

\$1/2 = 15 / "XZ"\$

Step

Cross multiply:

\$XZ = 15/(1/2)\$
\$XZ = 15 times 2\$
XZ = 30 inches

Step

Now, calculate cosine X:

\$cos(X) = "XY" / "XZ"\$
\$cos(X) = 1/2\$

Step

So, the cosine of angle X is \$1/2\$.

Choice.A

Correct representation using the cosine formula

\$1/2\$

Choice.B

The cosine function only outputs values between -1 and 1. Therefore, -2 is not a possible value for the cosine function so wrong

-2

Choice.C

This is incorrect. It states \$−1/2\$, which is the cosine of 60 degrees, not 30 degrees

\$-1/2\$

Choice.D

The cosine of an angle cannot be greater than 1 or less than -1 because the cosine function’s range is between -1 and 1 so wrong

Answer

Option

Sumup

Can you briefly tell me what you’ve learned and understood in today’s lesson?