4.8 Solving Problems with Trigonometry

What you’ll learn about More Right Triangle Problems Simple Harmonic Motion … and why These problems illustrate some of the better-known applications of trigonometry.

Angle of Elevation, Angle of Depression Angle of Elevation: angle above the horizon that the eye has to look up to see something. has to look up to see something. Angle of Depression: angle below the horizon that the eye has to look down at something. has to look down at something.

Using Angle of Elevation The angle of elevation from the buoy to the top of the Barnegat Bay lighthouse 130 feet above the surface of the water is 5 º. Find the distance x from the base of the lighthouse to the buoy. 130 x 5º5º 1. Draw the picture 2. Write the equation. 3. Solve for the unknown variable.

Using Angle of Elevation 1. If the height of a building is 470 m and you are standing 100 m away from the building, find the angle of elevation to the top of the building. Your Turn:

Indirect Measurements 1. Draw the picture. A car is observed with an angle of depression of 22 degrees from the top of a 300 foot building. A little later, the care is from the top of a 300 foot building. A little later, the care is observed from the same location with an angle of observed from the same location with an angle of depression of 46 degrees. How far did the car travel? depression of 46 degrees. How far did the car travel? 22º 46º 300’ 22º x = ? 46º

22º 46º 300’ 22º x = ? 46º a b 22º 300’ 300’ x = b – a x

a b 46º 22º 300’ 300’ x = b – a x x = 452.8’

Your turn: A large balloon is attached to the ground with a cable. The angle of elevation from you to the balloon is 35º. You walk 20’ closer to the balloon. The new angle of elevation is now 40º. How high is the balloon above elevation is now 40º. How high is the balloon above the ground? the ground?2.

Simple Harmonic Motion Period: length of horizontal axis encompassing one complete cycle = one complete cycle = Frequency =

Calculating Harmonic Motion A mass oscillating up and down on the bottom of a spring can be modeled as harmonic motion (assuming perfect elasticity and no friction or air resistance). If the weight is displaced a maximum of 4 cm, find the modeling equation if it takes 3 seconds to complete one cycle. 1. Draw the picture. time y-axis: Distance below spring attachment point. spring attachment point. x-axis: time distance 4” 0 3 sec 4” 2. Write the equation.

Calculating Harmonic Motion 1. Draw the picture. time y-axis: Distance below spring attachment point. spring attachment point. x-axis: time distance 4” 0 3 sec 4” 2. Write the equation. 3. Solve the equation. Amplitude = 4”

HOMEWORK Section 4-8 (page 431) (evens) 2-26, 28a, 28b, 28c, 30 (17 problems)