ESC 251 HW 12 Due: Oct. 2

1)
(6 pts) Write a Fortran90 program that does the following:
a)
Asks the user to input three lengths a, b, and c
b)
Tests to determine if these lengths are capable of forming a triangle.
c)
If a triangle cannot be formed, an error message should be printed out. If (and only if) a triangle can be formed, your program should compute the area of the triangle using Heron's formula

where s is the semi-perimeter of the triangle

Test your program with the 3 sets of data: a = 4.1, b = 6.4, c = 10.1; a = 7.8, b = 12.0, c = 3.4 and a = 1.1, b = 2.2, c = 3.3. Extra credit (1 pts) if you can do this problem with only 1 IF statement with no compound testing.
2)
(5 pts) (Problem 3-9 in the book). The income tax in Australia is computed according to the following table:
 Taxble Income Tax Owed $0 -$6,000 $0$6,001 - $20,000$0.17 for each $1 over$6,000 $20,001 -$50,000 $2,380 plus$0.30 for each $1 over$20,000 $50,001 -$60,000 $11,380 plus$0.42 for each $1 over$50,000 over $60,000$15,580 plus $0.47 for each$1 over $60,000 In addition, a 1.5% tax is charged on all income regardless of the taxable amount. Write a program that will compute the income tax owed given the amount of taxable income. Test your program for income amounts of$5,015, $14,678,$55,784 and \$75,000.
3)
(6 pts) When a light ray pssses from one medium to another, the light ray gets bent. Snell's Law of Refraction is the relationship that determines how much a light ray will bend. It states

where is the angle of incidence through a medium with a refractive index of n1 and is the angle of refraction through a medium with a refractive index of n2.

Write an F90 program that will ask the user to input values of (in degrees), n1 and n2 and computes the value of (provided the calculation is feasible). The value of should be printed out in degrees. In the event that the calculation is not feasible, an error message should be printed out.

Test your program using the 2 cases

a)
b)