In any , prove the following:

Question 1: In , if and , show that the area is sq. units.

Answer:

The area of a triangle is given by

Therefore Area sq units.

Question 2: In , if and , show that the area is sq. units.

Answer:

The area of a triangle is given by

Question 3: The sides of a triangle are and , show that: .

Answer:

Given and

LHS

RHS. Hence proved.

Question 4: In , if , find and .

Answer:

Given and

Question 5:

Answer:

RHS

LHS. Hence proved.

Question 6:

Answer:

LHS

RHS. Hence proved.

Question 7:

Answer:

LHS

Question 8:

Answer:

Hence proved.

Question 9:

Answer:

LHS

RHS. Hence proved.

Question 10:

Answer:

In , we have

LHS

RHS. Hence proved.

Question 11:

Answer:

LHS

RHS. Hence proved.

Question 12:

Answer:

We know

Hence proved.

Question 13:

Answer:

LHS

RHS. Hence proved.

Question 14: In prove that

Answer:

LHS

RHS. Hence proved.

Question 15: In any , , then prove that

Answer:

Let

Adding all the three

or

Question 16: In any , if , prove that

Answer:

Given

Now

Hence proved.

Question 17: In any , , prove that the triangle is right angled.

Answer:

This means either

Hence one of the angles is . Therefore the triangle is a right angled triangle.

Question 18: In any , if , prove that the triangle is isosceles.

Answer:

Using sine rule,

Now

the triangle is Isosceles.

Question 19: Two ships leave a port at the same time. One goes km/hr in the direction of and the other travels km/hr in the direction of . Find the distance between the ships at the end of hrs.

Answer:

Let and be the position of two ships at the end of hours.

km

km

Using cosine formula in

km