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Hi - Thank you for the kind words! If you carefully look at △CEB, it is actually a right triangle because ∠CEB is a right angle since CE is perpendicular to AB. In a right triangle, the Cosine ratio of an acute angle = adjacent side / hypotenuse. In the right triangle △CEB, the adjacent side for ∠CBE (which is equal to 60°) is EB and the hypotenuse is BC. That's why, in △CEB, Cos 60° = EB/BC. Hope it is clear now. Appreciate your blessings & support !!!

​@@finemath You're welcome, anytime for the kind words! Wow, I'm stunned at how well you expounded it in the video and how I somehow didn't understand it the first time; when I was in the middle of reading your compendious explanation, I scrolled back to the video, it all clicked, and I solved the problem in about 25-30 seconds. It's crystal-clear now, for you made it a seemingly difficult problem become relatively easy! You're very welcome; your pure-hearted help is admirable and exemplary, so please firmly grasp it forevermore!

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Hi - Thank you for your support & feedback! I am planning to complete the theory portion first. After that, I will do the PYQ's.

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Hi - In fact I could have stopped at 10:13 because the expression was reduced to a simple enough form. That form can be used if we are given: R, A, B and C. However, I decided to continue a little further to express it in terms of the circumradius and the radius of the 1st excircle. So, we should use whichever expression/formula is most suitable depending on the info provided in the actual question. Thank you for your support!

@@finemath OK

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Hi - Your approach will work fine, too. In fact all of these formulae are inter-connected. For example:- Let's assume, a, b, C are given. Using Cosine Law, we can easily calculate the value of the 3rd side length c. After that, to find the angle A, as you have suggested, ∆ = (1/2)bcSinA => SinA = 2∆/bc Now, if we substitute ∆ with (1/2)abSinC, we will get:, SinA = 2((1/2)abSinC)/bc = (a/c)SinC which is what I have derived in the video. So, whichever way we go, we will get the same result. :) In the real exam paper, based on the provided data, take whichever approach would make the calculation easy or whichever approach you are most comfortable with. Thank you for your support!

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Hi - The "n" here is the "degree of the polynomial expression/function". The degree of a polynomial is the highest exponent of the variable 'x' in the expression/function. For example, what is the degree of the polynomial expression: 10 + 9x + 3x^5 - 7x^2 + 11x^4 ? Well, among the five terms, the 3rd term has the highest degree/exponent of x which is 5. Therefore, the degree of this polynomial expression is actually 5. Hope it's clear now!

Hi - I have not done any videos on Trigonometric Inequalities yet. I plan on doing it after I start working on Function graphs (right before Calculus). Though some simple Trigonometric Inequalities can be solved with the help of Unit Circle, more complex Trigonometric Inequalities will require trigonometric function graphs to easily understand the solutions set. Thank you for your support!!!

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You are absolutely correct! Thank you!

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That's right! :)

Good job! The correct answer option can be found that way, too! Thank you!

I agree, many of the practice problems (including this one) can be solved without a paper & pencil. In the real ACT exam, we should try & find the correct answer as quickly as possible. In fact, majority of the problems can be solved in our brain/mind. Thank you for visiting, and thank you for your support!!!

The difference between the act and the actual problem is you have the possible answers. My strategy for long or difficult problems is getting the question to a form where plug and chug works. It is usually faster than trying 2 or 3 different ways to remember how to solve a tricky question.

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Thank you! Happy learning!