Question

NO LINKS!! URGENT HELP!!!

Please help me with this problem.

Answer 1

Yes

Explanation:

So we have right triangle with hypotenuse is the ladder which is 18 ft and a leg of the triangle which is 6 ft

cos(angle) = 6/18 = 1/3

angle = cos^-1(1/3) = 70.53°

Since 70.53° is less than 75°, it is considered safe under the guidelines mentioned.

Answer 2

Yes, Mr Smith's placement of his ladder will be considered safe under the given guidelines.

Explanation:

To determine if Mr. Smith's ladder placement is safe, we can model the given scenario as a right triangle, and calculate the angle the ladder makes with the ground using trigonometry.

Let θ be the angle the ladder makes with the ground (in degrees).

The distance from the base of the ladder to the house (6 feet) is the side adjacent angle θ.

The length of the ladder (18 feet) is the hypotenuse of the right triangle.

As we have the hypotenuse and the side adjacent to the angle, we can use the cosine trigonometric ratio to find the measure of the angle.

`\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=(A)/(H)$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}`

Substitute A = 6 and H = 18 into the cosine ratio and solve for θ:

`\cos(\theta)=(6)/(18)`

`\theta=\cos^(-1)\left((6)/(18)\right)`

`\theta=70.528779...^(\circ)`

`\theta=70.53^(\circ)\; \sf (2\;d.p.)`

The calculated angle the ladder makes with the ground is 70.53° (to two decimal places). As this angle less than the recommended maximum angle of 75°, Mr. Smith's ladder placement can be considered safe under the given guidelines.