IDNLearn.com: Your trusted source for finding accurate and reliable answers. Our community is ready to provide in-depth answers and practical solutions to any questions you may have.
Sagot :
To determine the triangle where the angle [tex]\( x \)[/tex] is equal to [tex]\( \tan^{-1}\left(\frac{3.1}{5.2}\right) \)[/tex], we need to focus on the relationship between the sides of the right triangle and the angle [tex]\( x \)[/tex].
### Step-by-Step Solution:
1. Definition of the Tangent Function:
The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. Mathematically:
[tex]\[ \tan(x) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]
2. Given Information:
We are given that:
[tex]\[ x = \tan^{-1}\left(\frac{3.1}{5.2}\right) \][/tex]
3. Calculate [tex]\( x \)[/tex]:
From this relationship, we know that [tex]\( x \)[/tex] is the angle whose tangent is [tex]\(\frac{3.1}{5.2}\)[/tex].
4. Angle in Degrees:
The value of [tex]\( x \)[/tex] in degrees can be found using the arctangent function (inverse tangent). From the result, we know:
[tex]\[ x \approx 30.80144597613683^\circ \][/tex]
5. Angle in Radians:
Similarly, the value of [tex]\( x \)[/tex] in radians is:
[tex]\[ x \approx 0.5375866466587464 \text{ radians} \][/tex]
6. Identifying the Triangle:
To find the triangle with this angle, look for a right triangle where the ratio of the side lengths (opposite to [tex]\( x \)[/tex] over adjacent to [tex]\( x \)[/tex]) is [tex]\(\frac{3.1}{5.2}\)[/tex].
Thus, the triangle you are looking for is a right triangle with an angle [tex]\( x \approx 30.8^\circ \)[/tex] or [tex]\( x \approx 0.538 \text{ radians} \)[/tex] such that:
[tex]\[ \tan(x) = \frac{3.1}{5.2} \][/tex]
You will find [tex]\( x \)[/tex] in the triangle where:
- The length of the side opposite [tex]\( x \)[/tex] is [tex]\( 3.1 \)[/tex],
- The length of the side adjacent to [tex]\( x \)[/tex] is [tex]\( 5.2 \)[/tex],
or any triangle with a proportional relationship (similar triangles) to these side lengths.
### Step-by-Step Solution:
1. Definition of the Tangent Function:
The tangent of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side. Mathematically:
[tex]\[ \tan(x) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]
2. Given Information:
We are given that:
[tex]\[ x = \tan^{-1}\left(\frac{3.1}{5.2}\right) \][/tex]
3. Calculate [tex]\( x \)[/tex]:
From this relationship, we know that [tex]\( x \)[/tex] is the angle whose tangent is [tex]\(\frac{3.1}{5.2}\)[/tex].
4. Angle in Degrees:
The value of [tex]\( x \)[/tex] in degrees can be found using the arctangent function (inverse tangent). From the result, we know:
[tex]\[ x \approx 30.80144597613683^\circ \][/tex]
5. Angle in Radians:
Similarly, the value of [tex]\( x \)[/tex] in radians is:
[tex]\[ x \approx 0.5375866466587464 \text{ radians} \][/tex]
6. Identifying the Triangle:
To find the triangle with this angle, look for a right triangle where the ratio of the side lengths (opposite to [tex]\( x \)[/tex] over adjacent to [tex]\( x \)[/tex]) is [tex]\(\frac{3.1}{5.2}\)[/tex].
Thus, the triangle you are looking for is a right triangle with an angle [tex]\( x \approx 30.8^\circ \)[/tex] or [tex]\( x \approx 0.538 \text{ radians} \)[/tex] such that:
[tex]\[ \tan(x) = \frac{3.1}{5.2} \][/tex]
You will find [tex]\( x \)[/tex] in the triangle where:
- The length of the side opposite [tex]\( x \)[/tex] is [tex]\( 3.1 \)[/tex],
- The length of the side adjacent to [tex]\( x \)[/tex] is [tex]\( 5.2 \)[/tex],
or any triangle with a proportional relationship (similar triangles) to these side lengths.
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.