Two of a triangle's interior angles measure $45^{\circ}$ and $55^{\circ}$. If the triangle's side lengths are represented by a, b, and c and a<b<c, which of the following statements is true for this triangle? A. $a^{2}+b^{2}>c^{2}$, B. $a^{2}+b^{2}<c^{2}$, C. $a^{2}+b^{2}=c^{2}$, D. Not enough information to determine.

Solution

VerifiedBy Triangle Sum Theorem, the missing angle measures $180\text{\textdegree}-45\text{\textdegree}-55\text{\textdegree} =80\text{\textdegree}$. Since all angles are acute, then the triangle is an acute triangle.

By the Pythagorean acute inequality theorem, a triangle with side lengths $a$, $b$, and $c$ where $c$ is the longest side form an acute triangle if:

$a^2+b^2>c^2$

So, the correct answer is choice $\textbf{\color{#c34632}A.}$

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Geometry: Common Core, New York Edition

1st Edition•ISBN: 9780789189318 (1 more)Joyce Bernstein#### Big Ideas Math Geometry: A Common Core Curriculum

1st Edition•ISBN: 9781608408399 (1 more)Boswell, Larson## More related questions

1/4

1/7