In a triangle A B C, if A=18^∘, b-a=2, a b=4, then the triangle is (a) acute angled (b) right an

step 1 I have a given an triangle ABC angle is 18 degrees. Given this relation here, two relations here

In a triangle A B C, if A=18^∘, b-a=2, a b=4, then the...

Key Concepts

Algebraic Techniques in Geometry

Many geometric problems require the use of algebraic manipulation to establish relationships between different elements of a triangle. Techniques such as solving quadratic equations or systems of equations allow one to deduce side lengths or angle measures from given conditions, integrating algebra with geometric reasoning.

Triangle Classification

This concept involves categorizing triangles based on their angles (acute, right, and obtuse) and sides (scalene, isosceles, equilateral). Understanding these classifications helps in determining the inherent properties of triangles and guides the approach to solving geometric problems.

Trigonometric Relationships in Triangles

Trigonometric laws, such as the Law of Sines and the Law of Cosines, are fundamental in relating the angles and sides within triangles. These relationships are crucial for solving unknown measurements and for analyzing the triangle's structure when certain elements are given.

Transcript

00:01 I have a given an triangle abc angle is 18 degrees.

00:03 Given this relation here, two relations here, b and b and b.

00:07 And then i want to check here, whatever triangle it is.

00:11 So here we just use this b negative a equals to and ab equals four and find the value of a and b.

00:19 So we'll get here.

00:22 This will be, so maybe have this is, let's the b times.

00:29 And we have a from b times.

00:31 So we have a from here.

00:32 You substitution here, so a from here, that is given as b negative 2 equals 4.

00:38 So b square negative 2b, negative 4 is equal to 0.

00:45 So this is quite a formula, 2 positive negative square root b square, negative 4ac, over 2, 2 positive 2 positive root 20, that is 2 root 5, over that's giving 1 positive negative root 5.

01:04 So let's see have b here.

01:08 So let's say check here b is equal to 1 negative root 5.

01:15 So b can't be negative.

01:16 So we'll go with here b equals 1 positive root 5 or we can say root 5 positive 1.

01:24 That's coming out to be b.

01:27 Next we have a is given as 4 over b.

01:32 Rationalize this.

01:37 So it's going to have to be root 5, negative 1.

01:43 Now, maybe angle a is 18 degrees.

01:45 So we use that.

01:47 So what we do here for that, and we have just idea about a and b.

01:51 So we can use sign rule.