I will give the brainliest and tons of points please hurry!

Joshua has a ladder that is 23 ft long. He wants to lean the ladder against a vertical wall so that The top of the ladder is 21.5 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 70°. Will the ladder be safe at this height?

Show your work and draw a diagram to support your answer. Round all answers to the nearest
hundredth.

To determine if the ladder is safe, we can model the given scenario as a right triangle, with the ladder (23 ft) representing the hypotenuse, and the vertical distance between the ground and the top of the ladder (21.5 ft) representing the side opposite the angle.

To find the angle of elevation of the ladder, we can use the sine trigonometric ratio:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Sine trigonometric ratio}}\\\\\sf \sin(\theta)=\dfrac{O}{H}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$\theta$ is the angle.}\\\phantom{ww}\bullet\;\textsf{O is the side opposite the angle.}\\\phantom{ww}\bullet\;\textsf{H is the hypotenuse (the side opposite the right angle).}\end{array}}[/tex]

In this case:

O = 21.5 ft
H = 23 ft

Substitute the values into the ratio and solve for angle θ:

[tex]\sin\theta=\dfrac{21.5}{23}\\\\\\\theta=\sin^{-1}\left(\dfrac{21.5}{23}\right)\\\\\\\theta=69.193052223...^{\circ}\\\\\\\theta=69.19^{\circ}\; \sf (2\;d.p.)[/tex]

As the angle of elevation is less that 70°, the ladder is safe at this height.