Question 1: If in a and ; find the ratios of their sides.

Answer:

and ;

Using Sine Rule,

Question 2: If in a , then find .

Answer:

Using sine rule,

Question 3: If in , if and and , then find and

Answer:

Given in , if and and

Using sine rule,

In any triangle ABC, prove the following:

Answer:

Answer:

Answer:

Dividing Numerator and Denominator by we get

Answer:

Dividing Numerator and Denominator by we get

Answer:

Answer:

Answer:

Answer:

Using cosine rule

LHS. Hence proved.

Answer:

Answer:

LHS. Hence proved.

Answer:

Answer:

Answer:

Answer:

Answer:

Answer:

Answer:

Answer:

Similarly.

and

Hence proved.

Answer:

Answer:

Answer:

Question 25: In prove that, if be any angle, then

Answer:

LHS. Hence proved.

Question 26: In , if , show that the triangle is a right angled.

Answer:

Let , and

Given

Since the triangle satisfies Pythagoras Theorem, the triangle is a right angles triangle.

Question 27: In any , if , prove that and are also in AP.

Answer:

Given

Question 28: The upper part of a tree broken over by the wind makes an angle of with the ground and the distance from the root to the point where the top of the tree touches the ground is . Using sine rule, find the height of the tree.

Answer:

Using sine rule,

Question 29: At the foot of the mountain the elevation of the peak is , after ascending towards the mountain up the slope of 30^o inclination, the elevation is found to be . Find the height of the mountain.

Answer:

Let

In

Therefore the height of triangle is

Question 30: A person observes the angle of elevation of the peak of a hill from a station to be . He walks c meters along a slope inclined at an angle and finds the angle of elevation of the peak of the hill as . Show that the height of the peak above the ground is

Answer:

The person is observing the peak from point

Distance traveled is and the angle of inclination is

Observing the peak from point , angle of inclination is

Now consider

… … … … … i)

Now consider

We know,

In

Now consider ,

Substituting the value of from i)

… … … … … ii)

We need to find the total height of the peak

… … … … … iii)

From ,

… … … … … iv)

From

… … … … … v)

Hence proved.

Question 31: If the sides of , prove that

Answer:

If sides

Using sine rule,