the distance between city a and city b is 22 miles. the distance between city b and city c is 54 miles. the…

the distance between city a and city b is 22 miles. the distance between city b and city c is 54 miles. the distance between city a and city c is 51 miles. what type of triangle is created by the three cities? an acute triangle, because 22² + 54²>51² an acute triangle, because 22² + 51²>54² an obtuse triangle, because 22² + 54²>51² an obtuse triangle, because 22² + 51²>54²

the distance between city a and city b is 22 miles. the distance between city b and city c is 54 miles. the distance between city a and city c is 51 miles. what type of triangle is created by the three cities? an acute triangle, because 22² + 54²>51² an acute triangle, because 22² + 51²>54² an obtuse triangle, because 22² + 54²>51² an obtuse triangle, because 22² + 51²>54²

Answer

Answer:

B. an acute triangle, because $22^{2}+51^{2}>54^{2}$

Explanation:

Step1: Recall triangle - type rules

For a triangle with side lengths $a$, $b$, and $c$ (where $c$ is the longest side), if $a^{2}+b^{2}>c^{2}$, the triangle is acute; if $a^{2}+b^{2}<c^{2}$, the triangle is obtuse; if $a^{2}+b^{2}=c^{2}$, the triangle is right - angled.

Step2: Identify the longest side

Given side lengths $22$, $51$, and $54$. The longest side $c = 54$, $a = 22$, and $b = 51$.

Step3: Calculate and compare

Calculate $a^{2}+b^{2}=22^{2}+51^{2}=484 + 2601=3085$ and $c^{2}=54^{2}=2916$. Since $22^{2}+51^{2}>54^{2}$, the triangle is acute.