Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides.
Trigonometry describe relationships andhave applicability to cyclicalphenomena, such as waves. It is usedextensively for astronomical studies andpractical art of surveying. It is used innavigation,measuring heights anddistances.
I never knewthat they areso many uses fortrigonometry
sin 30 =1/2 tan30=1/ 3 sin 45=1/ 2 tan45=1 sin 60=3/2 tan60= 3cos30= 3/2cos45=1/ 2cos60=1/2
The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer. Horizontal level
The angle of elevation of an object viewed,is the angle formed by the line of sight with the horizontal when it is above the horizontal level. Horizontal level
The angle of depression of an object viewed,us the angle formed by the line of sight with the horizontal when it is below the horizontal level. Horizontal level
An observer 1.5m tall is 28.5 m away from a building.the angle of elevation of the top of the building from its eyes is 45.what is the height of the building?
Here,AB is the tower ,CD is the observer and angle ADE is the angle of elevation. In this case ADE is a triangle,right-angled at E and we are required to find the height of the tower . * AB=AE+BE=AE+1.5 * DE=CB=28.5mNow, tan45=AE/DEi.e., 1=AE/28.5Therefore , AE=28.5mSo,the height of the tower(AB)=(28.5+1.5)m =30m
Tweety is flying at a certain height above the ground. suddenly she spots something peculiar on the ground. She bends her head forming an angle of 45.the object is placed 20m on the ground level. Find the height at which tweety is flying.
Here, AB is the height at which tweety is flying BC is the ground level .Angle DAC is the angle of depression .AC is the line of sight .Angle ACB=45. tan45=opp/adj =AB/CB 1 =AB/20 Therefore AB=20m So, height at which tweety is flying =20m