Download Lesson 6-3 Solving for Angle Measures

Math 2 Honors
Lesson 6-3: What is the Angle?
Name_________________________
Learning Goals:
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I can calculate sine and cosine ratios for acute angles in a right triangle when given two side lengths.
I can use side lengths to estimate angle measures.
I can solve right triangles by finding the measures of all sides and angles in the triangles.
I can use sine, cosine, tangent, and their inverses to solve for the unknown side lengths and angle
measures of a right triangle.
I can solve application problems involving right triangles, including angle of elevation and depression,
navigation and surveying.
1. In Lesson 6-2 you explored ways to use trigonometric functions to indirectly measure the height of
Chicago’s Bat Column sculpture. Cal read some literature that said the Bat Column’s height BD is
about 30 meters.
a. Cal sighted to the top of the sculpture from a point A, 25 meters from
point C and 1.5 meters above the ground. Use your calculator to guess
and check to find the approximate measure of angle A.
b. Suppose Cal sighted from a point 18 meters from point C and
1.5 meters above the ground. Use the same method as in Part a
to estimate the measure of the angle of elevation from this point.
2. Using your calculator, estimate (to the nearest degree) the measure of acute B for each of the
following trigonometric functions.
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1
a. sin B 
b. cos B 
c. tan B  2
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2
3. You can also use the inverse function capabilities of your calculator to produce the acute angle
measure when you know a trigonometric function value as in Problem 2. The function sin 1 (read
“inverse sine” or arcsine) is related to the sine function for acute angles in a way similar to the way
the square root and squaring operation are related. One function “undoes” the other. Thus, sin 1 x
is the acute angle whose sine is x. The inverse cosine or arccosine (denoted cos 1 ) and inverse
tangent or arctangent (denoted tan 1 ) are similarly related to the cosine and tangent functions.
Check your answers to number (2) by using the inverse trig functions.
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. Use the sin 1 function of your calculator to compute the
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measure of A. (Make certain your calculator is set in degree mode.)
a. Suppose you know sin A 
b. Use inverse trigonometric functions to find the measure of B that corresponds to each of
the function values given in Problem 2. Compare these values to the values you obtained in
that problem.
c. Use the calculator display at the right to find sin 37.5895029649.
d. Use your calculator to find the degree measure of the
acute angle in each of the following cases, where possible.
i.
iii.
tan B  1.84
sin A  2.15
ii.
sin A  0.852
iv.
cos B  0.213
4. House painters make decisions not only about the type of paint to use but also about what equipment
to use. Suppose a house painter needs to buy a new extension ladder that will reach up to a vertical
height of 30 feet when leaned against the side of a house. For safety reasons, it is recommended that
the ladder is placed so the angle it makes with level ground measures 75.
a. What is the minimum fully-extended length of a ladder that meets these requirements?
Draw a picture to help you set-up this problem!!!
b. Suppose the painter’s assistant extends the new ladder to 28 feet and leans it against a house
from a point 11.5 feet from the house. Draw a picture to help you set-up this problem!!!
i.
What angle does the ladder make with the ground?
ii.
At what vertical height from the ground does the ladder meet the side of the house?
iii.
To what length should the ladder be adjusted if it is to reach the same point on the side
of the house but make the recommended 75 angle with the ground?
iv.
How far will the ladder be placed from the house after it is adjusted as in part iii?