Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
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
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.
