Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Let's analyze the given distances to classify the triangle formed by the cities A, B, and C.
We are given:
- The distance between city A and city B (AB) = 22 miles.
- The distance between city B and city C (BC) = 54 miles.
- The distance between city A and city C (AC) = 51 miles.
To classify the triangle based on its angles, we'll use the properties of the squares of the sides and the Pythagorean theorem:
1. If [tex]\( a^2 + b^2 > c^2 \)[/tex], where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are the sides of the triangle, the triangle is acute.
2. If [tex]\( a^2 + b^2 < c^2 \)[/tex], the triangle is obtuse.
3. If [tex]\( a^2 + b^2 = c^2 \)[/tex], the triangle is right.
Calculating the squares of each side:
- [tex]\( AB^2 = 22^2 = 484 \)[/tex]
- [tex]\( BC^2 = 54^2 = 2916 \)[/tex]
- [tex]\( AC^2 = 51^2 = 2601 \)[/tex]
Now, let's compare the sums of the squares of two sides to the square of the third side to determine the type of triangle:
Step 1: Check [tex]\( AB^2 + BC^2 \)[/tex] and compare it to [tex]\( AC^2 \)[/tex]:
- [tex]\( AB^2 + BC^2 = 484 + 2916 = 3400 \)[/tex]
- [tex]\( AC^2 = 2601 \)[/tex]
Since [tex]\( 484 + 2916 > 2601 \)[/tex]:
- [tex]\( 22^2 + 54^2 > 51^2 \)[/tex]
This comparison indicates that the triangle is obtuse.
Therefore, the triangle formed by the cities A, B, and C is an obtuse triangle. The correct statement is:
"An obtuse triangle, because [tex]\(22^2+54^2 > 51^2\)[/tex]"
We are given:
- The distance between city A and city B (AB) = 22 miles.
- The distance between city B and city C (BC) = 54 miles.
- The distance between city A and city C (AC) = 51 miles.
To classify the triangle based on its angles, we'll use the properties of the squares of the sides and the Pythagorean theorem:
1. If [tex]\( a^2 + b^2 > c^2 \)[/tex], where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are the sides of the triangle, the triangle is acute.
2. If [tex]\( a^2 + b^2 < c^2 \)[/tex], the triangle is obtuse.
3. If [tex]\( a^2 + b^2 = c^2 \)[/tex], the triangle is right.
Calculating the squares of each side:
- [tex]\( AB^2 = 22^2 = 484 \)[/tex]
- [tex]\( BC^2 = 54^2 = 2916 \)[/tex]
- [tex]\( AC^2 = 51^2 = 2601 \)[/tex]
Now, let's compare the sums of the squares of two sides to the square of the third side to determine the type of triangle:
Step 1: Check [tex]\( AB^2 + BC^2 \)[/tex] and compare it to [tex]\( AC^2 \)[/tex]:
- [tex]\( AB^2 + BC^2 = 484 + 2916 = 3400 \)[/tex]
- [tex]\( AC^2 = 2601 \)[/tex]
Since [tex]\( 484 + 2916 > 2601 \)[/tex]:
- [tex]\( 22^2 + 54^2 > 51^2 \)[/tex]
This comparison indicates that the triangle is obtuse.
Therefore, the triangle formed by the cities A, B, and C is an obtuse triangle. The correct statement is:
"An obtuse triangle, because [tex]\(22^2+54^2 > 51^2\)[/tex]"
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.