Geometry Question Help

Question

A fire department’s longest ladder is 140 feet and the safety regulation states that they can use it for rescues up to 110 feet off the ground. What is the maximum safe angle the rescue ladder can make with the ground?  

Answer 1

Draw a picture to help you visualize this.

The ladder will be resting on the ground (some distance away from a building or tree or whatever) and, at the top, it will rest against the structure. So, the ladder creates a diagonal line segment. The structure itself is a vertical line segment. The point where the bottom of the ladder meets the ground is horizontal from the bottom the structure, connecting those 2 points creates a horizontal line segment. Now you have a right triangle. The ladder is 140 ft long, so the hypotenuse of the triangle is 140 feet long.

The question says that rescues can be no higher than 110 feet off the ground, so the vertical segment has a maximum length of 110 ft.

When the hypotenuse is 140 and the vertical leg is 110, what is the angle made by the bottom of the ladder & the ground? Use a trig function to find the answer. The vertical leg is the side opposite this angle and then we have the hypotenuse. [Opposite/Hypotenuse] = sine of the angle

Sin(x) = 110/140

Sin(x) = 11/14

Sin^-1(11/14) = ?

Approximately 51.8°

Answer 2

sine of the angle = 110/140

the angle = about 51.8 degrees

use a calculator with an inverse trig function