Question

if three sides of a triangle are 1 sin theta cos theta then the greatest angle of the triangle is​

Answer 1

Answer:

Greatest angle of the triangle is 90°.

Step-by-step explanation:

Given:

Three sides of the Triangle are $1\:,\:sin\,\theta\:,\:cos\,\theta$

To find: the greatest angle of the triangle.

 

To find greatest angle, first we find the type of triangle.

We know that if a , b  and c are sides of triangle,

If a² < b² + c² then triangle is acute angled triangle.

If a² = b² + c² then triangle is right angled triangle.

If a² > b² + c² then triangle is obtuse angled triangle.

We know that maximum value of sin x and cos x is 1.

So, value of $sin\,\theta\:,\:cos\,\theta$ will be less than or equal to 1

Using above mentioned result we get,

a² = 1² = 1

$b^2+c^2=sin^2\,\theta+cos^2\,\theta=1$

As, a² = b² + c²

Triangle is right angled.

⇒ Greatest angle is right angle or 90°

Therefore, Greatest angle of the triangle is 90°.