Some problems on Trigonometry

Do you know a fact guys, how was the measurement of heights and distance of an object were calculated in the ancient times? No idea right..i am sure you are not aware of it, even for me it was a new thing to know. Trigonometry, yes friends it was calculated with the help of trigonometry.

Look for some trigonometry worksheets and work on them, to increase your knowledge. I have a few solved problem that will help you. Introduction to trigonometry is already given to you in my previous post, check that as well. Look below for some solved trigonometry problems.

Problem No1.

Let’s assume that the distance of a person from a tower is 100 m and the angle subtended by the top of the tower with the ground is 30^o, now let’s calculate what the height of the tower in meters is? Below are the steps to solve the problem.

Steps:

1. Draw a simple diagram to represent the problem. Label it carefully and clearly mark out the quantities that are given and those which have to be calculated. Denote the unknown dimension by say h if you are calculating height or by x if you are calculating distance.
2. Identify which trigonometric function represents a ratio of the side about which information is given and the side whose dimensions we have to find out. Set up a trigonometric equation.
3. Substitute the value of the trigonometric function and solve the equation for the unknown variable.

Solution:

1. AB = distance of the man from the tower = 100 m
2. BC = height of the tower = h (to be calculated)
3. The trigonometric function that uses AB and BC is tan A, where A = 30^o.
4. So tan 30^o = BC/AB=h/100

Therefore we conclude height of the tower h= 100 tan 30^o = (100)/√3 =57.74m.

Problem No 2:-

Prove the given trig expression 1 + cot A/ 1 + tan A = 1 + cos A/ sin A + tan A

Solution:

Given

1 + cot A/ 1 + tan A = 1 + cos A/ sin A + tan A

Let us take L.H.S and we prove the R.H.S

L.H.S = 1 + cot A/ 1 + tan A

Here cot A = 1/ tan A

= 1 + (1/ tan A) / 1 + tan A

= (tan A + 1/ tan A) / 1 + tan A

= 1 + tan A/ (1 + tan A) tan A

L.H.S = cot A

R.H.S = 1 + cos A/ sin A + tan A

= 1 + cos A/ (sin A + (sin A/ cos A))

= 1 + cos A/ (sin A cos A + sin A/ cos A)

= 1 + cos A/ sin A(cos A + 1)/cos A

= (1 + cos A) cos A/ (cos A + 1) sin A

= cos A / sin A

R.H.S = cot A

Hence L.H.S = R.H.S

These problems will give you a clear idea on how to solve problems on trigonometry, but that is of no use until you don't work on it so what are you waiting for, start working on it immediately. Let me know how informative you found this post.