Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Triangle ABC is a right triangle and cos(22.6o)=StartFraction b Over 13 EndFraction. Solve for b and round to the nearest whole number.

Triangle A B C is shown. Angle A C B is 90 degrees and angle C A B is 22.6 degrees. The length of hypotenuse A B is 13 centimeters, the length of A C is b, and the length of C B is a.

Which equation correctly uses the value of b to solve for a?

tan(22.6o) = StartFraction a Over 13 EndFraction
tan(22.6o) = StartFraction 13 Over a EndFraction
tan(22.6o) = StartFraction a Over 12 EndFraction
tan(22.6o) = StartFraction 12 Over a EndFraction


Sagot :

In the given triangle ABC right angled at C and [tex]AC = b[/tex] and [tex]CB = a[/tex], the equation using value of b used for solving for a will be [tex]tan(22.6degrees) = \frac{a}{12}[/tex].

According to the question statement, Triangle A B C is shown. Angle A C B is [tex]90[/tex] degrees and angle C A B is [tex]22.6[/tex] degrees. The length of hypotenuse A B is [tex]13[/tex] centimeters, the length of A C is b, and the length of C B is a.

We are supposed to find the equation using value of b used for solving for a.

Solution: Given,

  [tex]AB = 13cm\\AC = b\\BC = a\\Angle BAC = 22.6degrees[/tex]

If hypotenuse is 13cm then value of b is either 5 or 12 as per Pythagorean Triplet. As there is no value such as 5 in the given options we take the value of [tex]b=12 cm[/tex].

[tex]cos(22.6degrees) = \frac{b}{13} =\frac{12}{13} \\sin(22.6degrees) = \frac{a}{13}\\[/tex]

Using the above two equations,

[tex]tan(22.6degrees)=\frac{a}{b} \\b=12\\tan(22.6degrees)=\frac{a}{12}[/tex]

Therefore option three "tan(22.6o) = StartFraction a Over 12 EndFraction" is the correct answer.

  • Pythagorean Triplet: If a, b and c are three sides of a right angled triangle, c being the hypotenuse then [tex]a^{2} +b^{2} =c^{2}[/tex] and a and b being either of the base and perpendicular.

To learn more about Pythagoras theorem, click on the link given below:

https://brainly.com/question/343682

#SPJ9

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.