Questions: If the angle made by the ladder with the ground is 30°, find the distance between the wall and the ladder if the height of the wall between the ground and the point of contact of the ladder is 15 ft.

If the angle made by the ladder with the ground is 30°, find the distance between the wall and the ladder if the height of the wall between the ground and the point of contact of the ladder is 15 ft.

Transcript text: If the angle made by the ladder with the ground is $30^{\circ}$, find the distance between the wall and the ladder if the height of the wall between the ground and the point of contact of the ladder is 15 ft.

Solution

Solution Steps

Step 1: Define the trigonometric ratio

We are given the angle between the ladder and the ground (30°), and the height of the wall (15 ft), which is the side opposite to the given angle. We need to find the distance between the wall and the ladder, which is the adjacent side to the given angle. The trigonometric ratio that relates the opposite and adjacent sides to an angle is tangent:

tan(angle) = opposite / adjacent

Step 2: Set up the equation

In our case, the angle is 30°, the opposite side is 15 ft, and the adjacent side is the distance we want to find (let's call it 'x'). So we have:

tan(30°) = 15 ft / x

Step 3: Solve for x

We know that tan(30°) = 1/√3 or √3/3. Substituting this value into the equation:

1/√3 = 15 / x

Multiplying both sides by x and by √3, we get:

x = 15√3 ft