Karen has a ladder that is 18 feet long. She wants to lean the ladder against a vertical wall so that the top of the ladder is 17.3 feet above the ground. For safety reasons, she wants the angle the ladder makes with the ground to be no greater than 75°. Will the ladder be safe at this height ? Show work
+561 The ladder forms a right-angle triange with the ground and the wall.
Looking at the angle between the ladder and the ground, this means the ladder is the hypotenuse, the wall is the opposite side, and the ground is the adjacent side.
We know the length of the ladder (18 ft) and the height of the wall (17.3 ft), so we know the hypotenuse and opposite side lengths, so we can use sin to calculate what the angle between the ladder and the ground would have to be.
\(\sin(\theta)=\frac{opposite}{hypotenuse}\)
\(\theta=\arcsin(\frac{opposite}{hypotenuse})\)
\(\theta=\arcsin(\frac{17.3}{18})\)
\(\theta=74.0^{\circ}\)
74 is less than 75, so the ladder will be safe.
+561 The ladder forms a right-angle triange with the ground and the wall.
Looking at the angle between the ladder and the ground, this means the ladder is the hypotenuse, the wall is the opposite side, and the ground is the adjacent side.
We know the length of the ladder (18 ft) and the height of the wall (17.3 ft), so we know the hypotenuse and opposite side lengths, so we can use sin to calculate what the angle between the ladder and the ground would have to be.
\(\sin(\theta)=\frac{opposite}{hypotenuse}\)
\(\theta=\arcsin(\frac{opposite}{hypotenuse})\)
\(\theta=\arcsin(\frac{17.3}{18})\)
\(\theta=74.0^{\circ}\)
74 is less than 75, so the ladder will be safe.
