Question

question 1-5
a ladder leans against a wall so the top of the ladder is 3.6 meters above the ground. if the angle between the ladder and the wall is 23°, how far is the base of the ladder from the wall to the nearest tenth of a meter?
enter the correct answer in the box.
meters

Explanation:

Step1: Identify the trigonometric relationship

We have a right triangle where the height on the wall (adjacent side to the angle) is 3.6 meters, the angle between the ladder (hypotenuse) and the wall is \(23^\circ\), and we need to find the distance from the base of the ladder to the wall (opposite side to the angle). We use the tangent function, which is \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). Let \(x\) be the distance from the base to the wall. So \(\tan(23^\circ)=\frac{x}{3.6}\).

Step2: Solve for \(x\)

Rearrange the formula to solve for \(x\): \(x = 3.6\times\tan(23^\circ)\). Calculate \(\tan(23^\circ)\approx0.4245\). Then \(x = 3.6\times0.4245\approx1.5282\). Rounding to the nearest tenth, we get \(x\approx1.5\).

Answer:

\(1.5\)