4.8 - Applications and Models (Story Problems)

Sections 4.8 explains how to use trigonometric functions to model and solve "real-life" problems

Some useful things to know in this section are angle of elevation and angle of depression.

• Angle of Elevation  is the term that denotes the angle from the horizontal, upward to an object.

Picture Source

• Angle of Depression is the term that denotes the angle from the horizontal, downward to an object.

Picture Source

Here is an example problem from the textbook of when to use angle of elevation

• A safety regulation states that the maximum angle of elevation for rescue ladder is 72°. If a fire department's longest ladder is 110 feet, what is the maximum safe rescue height?

So from this picture and the problem we are solving for "a". From the equation sin A = a/c, we can conclude that a = c sinA. So a = 110 sin 72° ≈ 104.6. So, the maximum safe rescue height is about 104.6 feet above the height of the truck.

Trigonometry and Bearings

In surveying and navigation, directions are generally given in terms of bearings. A bearing measures the acute angle a path or line of sight makes with a fixed north-worth line.

For instance, the bearing of S 35° E means 35 degrees east of south

When dealing with bearings often time you'll be given a measurement like this: 39° 45' l

In this case the angle measurement would be (39 + 45/60)°