Lesson 2 High Tide Solidify Understanding

Ready

Recall that the right triangle definition of the tangent ratio is:

a right triangle with angles labeled a, b, and c

1.

Solve for . Then find and .

a right triangle with a base of 56 centimeters and a hypotenuse of 65 centimeters. The height is labeled y. Angle C is 90 degrees and angles A and B are undetermined.

2.

Solve for . Then find and .

a right triangle with a height of 9 feet and a hypotenuse of 41 feet. The base is labeled x. Angle C is 90 degrees and angles A and B are undetermined.

3.

Solve for . Then find and .

a right triangle with a base of 21 feet and a hypotenuse of 29 feet. The height is labeled y. Angle C is 90 degrees and angles A and B are undetermined.

4.

Solve for . Then find and .

a right triangle with a base of 28 meters and a hypotenuse of 53 meters. The height is labeled y. Angle C is 90 degrees and angles A and B are undetermined.

Set

Many real-life situations such as sound waves, weather patterns, and electrical currents can be modeled by sine and cosine functions. The table shows the depth of water (in feet) at the end of a wharf as it varies with the tides at various times during the morning.

(time)

midnight

a.m.

a.m.

a.m.

a.m.

a.m.

noon

(depth)

5.

Sketch the line that shows the average depth.

a scatter plot with the y axis labeled in feet and the x axis labeled in time of day. The points resemble a sine curve. midnight6 A.M.noon2 ft8 ft16 ft

6.

Find the amplitude.

7.

Find the period. . Since a normal period for sine is , the new period for our model will be , so .

8.

High tide occurred hours after midnight. The formula for the displacement is . Use and solve for .

9.

Now that you have your values for , , , and , put them into an equation.

10.

Use your model to calculate the depth at 9 a.m. and 3 p.m.

a.

b.

11.

A boat needs at least feet of water to dock at the wharf. During what interval of time in the afternoon can it safely dock?

Go

Use the given solutions of a quadratic function and the -intercept to find the original equation.

12.

with -intercept

13.

with -intercept

14.

with -intercept

15.

with -intercept