Respuesta :
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
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