Question 1: In a right angles triangle , right angled at , if , find all the six trigonometric ratios of .

Answer:

Therefore,

Answer:

By Pythagoras theorem, we have

Answer:

, therefore

Answer:

By Pythagoras theorem, we have

Answer:

By Pythagoras theorem, we have

LHS = RHS.

Hence proved.

Answer:

By Pythagoras theorem, we have

Therefore LHS = RHS. Hence proved.

Question 7: In the given figure, . Determine (

Answer:

By Pythagoras theorem, we have

Therefore:

,

i) is ii) is

Answer:

Answer:

RHS. Hence proved.

Answer:

Squaring on both sides,

Answer:

Answer:

Therefore LHS = RHS. Hence proved.

Answer:

Dividing both the numerator and denominator by we get

Answer:

Answer:

By Pythagoras theorem,

Answer:

By Pythagoras theorem we get

Answer:

By Pythagoras theorem we get

RHS =

Therefore LHS = RHS. Hence proved.

Answer:

Answer:

By Pythagoras theorem, we get

Question 20: If , find

Answer:

, find

Question 21: If are acute angles such that , then show that

Answer:

Since

(angles opposite equal sides of a triangle are equal)

Question 22: In a triangle, are acute angles such that , show that

Answer:

Given that

(angles opposite equal sides of a triangle are equal)

Question 23: If is an acute angle such that , find the value of

Answer:

Question 24: In adjoining figure, is right angles at is the midpoint of . , . Find

Answer:

By Pythagoras theorem

ii) By Pythagoras theorem