Right Triangle Analysis: Compare Angles ∢B and ∢A

Question

The triangle ABC is a right triangle.

Which angle is larger, B ∢B or A ∢A ?

AAABBBCCC

Video Solution

Solution Steps

00:00 Which angle is larger - A\B?
00:06 Right triangle according to the given
00:10 Sum of angles in a triangle equals 180
00:17 Let's substitute angle A
00:25 Let's isolate the sum of angles B+C
00:37 Sum of these angles equals 90
00:41 Therefore angle B must be less than 90
00:49 And this is the solution to the question

Step-by-Step Solution

In a right triangle ABC \triangle ABC , angle C ∢C is the right angle, which equals 90°. Therefore, the other two angles A ∢A and B ∢B must sum to 90°.

For any right triangle, if one acute angle is larger, the opposite side (leg) is longer. Conversely, if an angle is smaller, the opposing leg must be shorter.

Based on the triangle's diagram and fundamental right triangle properties, it appears that angle A ∢A is larger than angle B ∢B , given that larger angles oppose longer sides.

This conclusion follows from practical geometry, where angle recognition and placement determine relative size.

Therefore, we can conclude that A ∢A is greater than B ∢B , or A>B ∢A > ∢B .

Answer

∢A>∢B