Chapter 10 - NCPN

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After taking off, a commercial jet covers
a horizontal distance of 23,100 feet
during the first 45 seconds of flight
and climbs to a height of 3,040 feet
above the ground. What is the plane’s
angle of elevation during the first part
of the ascent. Explain why it might be
important to know the plane’s initial
angle of elevation.
Step 1 Understand the Problem
What is the relevant information
presented in the problem statement
What will you need to calculate to solve
the problem
Step 2 Develop a Plan
Problem-solving strategy: Use a diagram.
What kind of triangle can be used to model
the situation Drawing a diagram can help
you understand the problem and develop a
method to solve it.
Step 3 Carry Out the Plan
Model the problem situation with a diagram.
Use the diagram to help you set up and solve
a trigonometric equation for the jet’s angle of
elevation, x. Round your answer to the nearest
tenth of a degree.
Step 4 Check the Results
Check the angle measure by substituting it into
the equation and making sure the result is a
true number sentence.
Lesson Assessment
Think and Discuss
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1. What is the result when you simplify tan –1 (tan x) Explain.
2. Explain how to find the measure of the angle whose terminal side
intersects the unit circle at (0.5, 0.866).
3. If the lengths of the legs of a right triangle are known, how can
the measures of the acute angles of the triangle be found
4. Which inverse trigonometric function would you use to find the
measure of an acute angle in a right triangle if you know the
lengths of the hypotenuse and the side opposite the angle
5. How many values of x are there such that tan x = 0 Explain.
10.3 Inverse Trigonometric Functions 451