Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Answer:
The answer is C
Step-by-step explanation:
i got it right on edge
Side AB = 13.7 miles, ∠A = 33.3° , ∠B = 56.7°
The correct answer is an option (c) Side AB = 13.7 miles, angle A = 33.3 degrees, angle B = 56.7 degrees.
What is right triangle?
"It is a triangle whose one of the angle measures 90° "
What is hypotenuse?
"It is a longest side of the right triangle."
What is sine rule of triangle?
"For triangle PQR,
[tex]\frac{sinP}{p} =\frac{sinQ}{q} =\frac{sinR}{r}[/tex]
where side QR is p, side PQ is r, and side PR is q"
What is Pythagoras theorem?
"In right triangle, [tex]a^{2}+ b^{2}=c^{2}[/tex] where c is the hypotenuse, a, b are other two sides of right triangle. "
For given question,
We have been given a triangle ABC.
Angle C = 90°
This means, triangle ABC is a right triangle.
Hypotenuse side AB is c,
And side CB is a, side CA is b.
Also given that, Side BC = 7.50 miles, Side AC = 11.43 miles
⇒ a = 7.5 miles and b = 11.43 miles
First we find the hypotenuse AB using Pythagoras theorem.
Using Pythagoras theorem,
⇒ AB² = BC² + AC²
⇒ AB² = (7.50)² + (11.43)²
⇒ AB² = 56.25 + 130.65
⇒ AB² = 186.9
⇒ AB = 13.67 miles
⇒ c = 13.67 miles
Using sine rule for triangle ABC,
[tex]\Rightarrow \frac{sin~A}{a} =\frac{sin~B}{b}= \frac{sin~C}{c}\\\\\Rightarrow \frac{sin~A}{7.50} =\frac{sin~B}{11.43} =\frac{sin~C}{13.67}[/tex]
Consider,
[tex]\Rightarrow \frac{sin~A}{7.50} =\frac{sin~C}{13.67}\\\\\Rightarrow \frac{sin~A}{7.50} =\frac{sin~90}{13.67}\\\\\Rightarrow \frac{sin~A}{7.50} =\frac{1}{13.67}[/tex]
⇒ 13.67 × sin A = 7.50
⇒ sin A = 0.5486
⇒ ∠A = 33.3°
We know that the sum of all angles of triangle is 180°
⇒ ∠A + ∠B + ∠C = 180°
⇒ 33.3° + ∠B + 90° = 180°
⇒ ∠B + 123.3° = 180°
⇒ ∠B = 56.7°
Therefore, Side AB = 13.7 miles, ∠A = 33.3° , ∠B = 56.7°
The correct answer is an option (c) Side AB = 13.7 miles, angle A = 33.3 degrees, angle B = 56.7 degrees.
Learn more about Pythagoras theorem here:
https://brainly.com/question/343682
#SPJ2
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
