A 40-foot ladder is leaning against a wall. To use the ladder safely, the angle between the wall and the ladder must be no more than 15 degrees. A worker places the bottom of the ladder 12 feet from the wall, and begins to climb. is the worker safe?

No, because the angle between the wall and the ladder is 17.45°

Step-by-step explanation:

Let's first outline the parameters in this particular question

-- - the angle between the wall and ladder is 15°

-- - the ladder is 40 foot tall

---the bottom of the ladder is placed 12 feet from the wall.

With the above, we can conclude that the ladder placed against the wall formed a shape that has the look of a right angle triangle, where the length if the ladder is the hypotenuse, the distance between the foot of the ladder and the wal is the adjacent, and the height of ladder against the wall is unknown.

Let's now try to find the value of the unknown (in this case, the opposite of that triangle shape formed)

Using Pythagorean theorem, where c = √ (a² + b²)

(C is the hypotenuse, a and b are the adjacent and opposite respectively)

40² = 12² + x²

X² = 40² - 12²

X² = 1456

X = √1456

X = 38.2

Now to find the angle made by the wall and the ladder

Tan x = opp/adj

Tan x = 12/38.2

Tan x = 0.3141

X = tan inverse of 0.3141

X = 17.45° (the angle between the wall and the ladder)