PLEASE HELP ME WITH THIS1. Joshua has a ladder that is 12 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 11.8 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 75°. Will the ladder be safe at this height? Show your work and draw a diagram to support your answer.I don't understand how to answer this. Can someone please help and explain this to me?
Accepted Solution
A:
Let's start with the drawing. (See the drawing at the bottom of this answer.)
Draw a vertical segment. At the bottom endpoint, draw a horizontal segment to the right. The angle at the bottom left is a right angle. So far this should look like an "L" shape. The vertical segment is the wall, and the horizontal segment is the ground.
Now draw a segment that connects the right endpoint of the horizontal segment and the top endpoint of the vertical segment. Now you have a right triangle. The diagonal segment represents the ladder. The diagonal segment is the hypotenuse. Label the diagonal segment, the hypotenuse, 12 ft. Label the vertical segment, the wall, 11.8 ft.
The angle at the bottom right is A. It is the angle the ladder makes with the ground. This angle cannot be greater than 75 degrees.
Now we use trigonometry to find the measure of angle A.
For this right triangle, and its angle A, you have a hypotenuse that measures 12 ft, and an opposite leg that measures 11.8 ft. We need to find angle A. The trig ratio that relates the opposite leg and the hypotenuse is the sine.
[tex] \sin A = \dfrac{opp}{hyp} [/tex]
[tex] \sin A = \dfrac{11.8}{12} [/tex]
[tex] \sin A = 0.98333 [/tex]
Since the sine of angle A equals 0.98333, we use the inverse sine function to find the measure of angle A.
[tex] A = \sin^{-1} 0.98333 [/tex]
[tex] A = 79.5^\circ [/tex]
Answer: The angle the ladder makes with the ground is 79.5 degrees which is greater than 75 degrees, so the ladder it will be unsafe in this position.