As per the observations of a person, standing exactly midway between two towers, the top of the two towers are at ang1le of elevation of 22.5° and 67.5°. What is the ratio of the height of the taller tower to the height of the shorter tower?
7, 24, 25 is a Pythagorean triplet. Therefore, the given triangle is a right angled triangle.In a right-angled triangle, the median to the hypotenuse is half the hypotenuse and is also the circum-radius of the triangle.As the hypotenuse is 25, the circum radius is 12.5
1080 = $2 3$ $\times$ $3 3$ $\times$ 5. For any perfect square, all the powers of the primes have to be even numbers. So, if the factor is of the form $2^ a$ $\times$ $3^ b$ $\times$$ 5^ c$ . The values 'a' can take are 0 and 2, b can take are 0 and 2, and c can take the value 0. Totally there are 4 possibilities. 1, 4, 9, and 36.