Question

an outdoor movie screen is 30 ft. tall. it needs additional support to keep it upright and prevent it from leaning. the town has decided to attach 15 ft. metal brackets to the back of the screen. the best spot to anchor the brackets to the ground is 6 ft. from the base of the screen. how far from the ground should the brackets be attached to the frame of the screen to ensure that the screen is at a

Explanation:

Step1: Apply Pythagorean theorem

Let the height from the ground to the attachment point on the screen be \(h\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 15\) (length of the bracket, hypotenuse), \(a=6\) (distance from the base of the screen on the ground). So \(h=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 15\) and \(a = 6\) into the formula: \(h=\sqrt{15^{2}-6^{2}}=\sqrt{225 - 36}=\sqrt{189}\).
Simplify \(\sqrt{189}=\sqrt{9\times21}=3\sqrt{21}\approx13.75\)

Answer:

The brackets should be attached approximately \(13.75\) ft from the ground.