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