Final answer:
Joshua's 15 ft ladder, if leaned against the wall to reach a height of 14.8 ft, would be at an unsafe angle less than 70° and thus, is not safe to use in this manner.
Step-by-step explanation:
The student has asked whether Joshua's ladder, which is 15 feet long and is supposed to lean against a wall with the top at 14.8 feet above the ground, will be safe with an angle no greater than 70°. To determine this, we can use the trigonometric function cosine, which relates the adjacent side (the height at which the top of the ladder reaches the wall) to the hypotenuse (the length of the ladder) in a right-angled triangle. The cosine of the maximum safe angle (70°) should therefore be equal to or greater than the ratio of the height of the ladder against the wall (14.8 feet) to the length of the ladder (15 feet).
We calculate the cosine of 70°: cos(70°) ≈ 0.342. Then we calculate the ratio 14.8/15 which equals 0.9867. Since 0.9867 is much greater than 0.342, it means the ladder will form an angle that is less than 70°, which is not within the safe range as per Joshua's requirement.
Therefore, it is not safe for Joshua to lean the ladder in this manner because the angle formed will be steeper than the maximum safe angle of 70°, which may result in the ladder slipping.