Question
The shadow of a tower standing on level ground is found
to be 40 m longer when the Sun's altitude is 30° than when it was 45°. Find the height (in meters) of the tower.Solution
Let AB be the tower, BC be the shadow at 45°, and BD be the shadow at 30°. The shadow of a tower standing on a level ground is found to be 40 m longer when the sun's altitude is 30° than when it is 45°. i.e. CD = 40 m Let BC = x m In triangle ABC, we have Tan45 =AB/BC AB =x.      … (1) In triangle ABD, We have. Tan 30 =AB/BD 1/ √ 3 =AB/x+40 √ 3AB =x+40 X =√ 3AB-40 … (2) x = √ 3x-40 x=40/ (√ 3-1)  we multiply the numerator and denominator by the conjugate of the denominator: x=20 (√ 3+1). 
For 3x² − 10x − 8 = 0, find (1/α + 1/β).
In the question, two equations I and II are given. You have to solve both the equations to establish the correct relation between x and y.
I. 3x<...
I. 2x2 - 9 x + 9 = 0Â
II. 2y2 - 7 y + 3 = 0
I. 8x² - 74x + 165 = 0
II. 15y² - 38y + 24 = 0
I. 3x2 - 16x - 12 = 0
II. 2y2 + 11y + 9 = 0
In the question, two equations I and II are given. You have to solve both the equations to establish the correct relation between 'p' and 'q' and choose...
For what values of k does the equation x² – (k+1)x + k = 0 have two distinct real roots, both greater than 1?
l. x2 - 16x + 64 = 0
II. y2Â = 64
I. 66x² - 49x + 9 = 0
II. 46y² - 37y - 30 = 0
I. 3p² - 17p + 22 = 0
II. 5q² - 21q + 22 = 0
