Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,219

High Scohol Mathematics - Trignometry II

1. Using the formula sin(A-B) = sinAcosB - cosAsinB, find the value of sin 15°.

2. If

, and

, prove that

by using the formula

.

3. The measure of angle of depression of the bottom of a building on a level fround from the top of the tower is 60° . How far is the building from the tower?

4. A tower is 100/√3 meters high. Find the angle of elevation if the point of observation is 100 meters away from its foot.

5. As observed from the top of a light house, 100 meters high above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30°  to 45° . Determine the distance travelled by the ship during the period of observation.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

vichavicha

Member

Registered: 2008-12-05

Posts: 1

Re: High Scohol Mathematics - Trignometry II

Q3. Half the height of the tower.
Q5. 50 meters.

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Knowledge is Power !

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,219

Re: High Scohol Mathematics - Trignometry II

OOps! I am sorry, I forgot to mention in #3 that the tower is 50 meters high.
Regarding your solution to #5, the solution isn't right.
I shall wait for any other membet to attempt, else I shall post all the solutions (sans diagams )

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

rzaidan

Member

Registered: 2009-08-13

Posts: 59

Re: High Scohol Mathematics - Trignometry II

Hi  ganesh 
(1)               sin(15°)=sin(45°-30°)=sin(45°)cos(30°)-cos(45°)sin(30°

                               =(1/√2)(√3/2)-(1/√2)(½)=(√3-1)/2√2

salam

Fruityloop

Member

Registered: 2009-05-18

Posts: 143

Re: High Scohol Mathematics - Trignometry II

#3.   28.86751346 meters.
#4.   30°
#5.   73.2050808 meters.