Question

1. A statue creates a shadow that is 30 ft long. The angle of elevation of the sun is 50°.

Answer 1

1- Let the triangle be ABC, where A is the point of intersection between the shadow and the ground and BC the height of the statue.
The angle of elevation of the sun is equal to the angle CBA (corresponding), so we can write :

tan (50°) = CB (height of statue) / BA (length of shadow)


tan (50°) = CB/30 ==CB = 30 x tan (50°) = 30 x 1.1917 = 35.8 ft 


2 A- P =P₀ (1+i)ⁿ Where P₀ is the initial population, I the rate of growth of the population, P the population after a period of n years and n, the number of tears. (in the problem t = n)
 P = 8500 (1 + 4.5%)ⁿ . This is the requested answer (don't forget n=t)

2 B- When P =70,000
70,000 = 8,500(1+0.045)ⁿ . Divide both sides by 8500
70,000/8,500 = (1+0.045)ⁿ
2.108 = (1.045)ⁿ
ln(2.108) = n. ln(1.045) and n = t = 16.94 ≈ 20 years

3- Your 3rd question is full of error. Rewrite it and I will help you