In flying the 81 miles from Champaign to Peoria, a student pilot sets a heading that is 8° off course and maintains an average speed of 88 miles per hour. After 15 minutes, the instructor notices the course error and tells the student to correct his heading. Through what angle will the plane move to correct the heading and how many miles away is Peoria when the plane turns?

59.29 miles and 9.8°

Step-by-step explanation:

Given data:

Distance from Champaign to Peoria = 81miles

Plane speed = 88miles/hr

Time travelled = 15minutes

Angle of the plane = 8° off course

Solution:

Using consine rule

c² = a² +b² -2ab·cos(C)

where we have a=81, b=88/4 = 22, C=8°.

Input data into the formula.

c² = 81² +22² -2*81*22·cos(8°)

= 3515.685

c ≈ √(3515.685)

≈ 59.29 miles

Using sine rule.

sin(A)/a = sin(C)/c

sin(A) = (a/c)sin(C)

arcsin(81/59.29·sin(8°))

= 9.8°

The plane must turn at an angle of 9.8°

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x