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Write the three relationships that exist from Section 8.1 as learned in class.
1: Finding Side Lengths in Right Triangles
Find x, y, and z.
Example 2
Find u, v, and w.
Example 3:
Find the value of x. Give your answer in simplest radical
form.
Example 4
Find the value of x. Give your answer in simplest radical
form.
Example 5
Find the values of x and y. Give your answers in simplest
radical form.
Example 6
Find the values of x and y. Give your answers in
simplest radical form.
Example 7
Find the values of x and y. Give your answers in simplest radical
form.
Example 8
sin A =
cos A =
tan A =
Example 9
Find the length of BC.
Round to the nearest
hundredth.
Example 10
Find the length of JL.
Round to the nearest
hundredth.
Example 11
Find the measure of R and T
Example 12
Classify each angle as an angle of elevation or angle of depression.
1. 6
2. 9
Example 13
A plane is flying at an altitude of 14,500
ft. The angle of depression from the
plane to a control tower is 15°. What is
the horizontal distance from the plane
to the tower?
Example 14
A woman is standing 12 ft from a
sculpture. The angle of elevation from
her eye to the top of the sculpture is
30°, and the angle of depression to its
base is 22°. How tall is the sculpture to
the nearest foot?
Key
Write the three relationships that exist from Section 8.1 as learned in class.
1: Finding Side Lengths in Right Triangles
Find x, y, and z.
62 = (9)(x)
x=4
y2 = (4)(13) = 52
6 is the geometric mean of
9 and x.
Divide both sides by 9.
y is the geometric mean of
4 and 13.
Find the positive square root.
z2 = (9)(13) = 117
z is the geometric mean of
9 and 13.
Find the positive square root.
Example 2
Find u, v, and w.
92 = (3)(u)
u = 27
9 is the geometric mean of
u and 3.
Divide both sides by 3.
w2 = (27 + 3)(27) w is the geometric mean of
u + 3 and 27.
Find the positive square root.
v2 = (27 + 3)(3)
v is the geometric mean of
u + 3 and 3.
Find the positive square root.
Example 3:
Find the value of x. Give your answer in simplest radical
form.
Example 4
Find the value of x. Give your answer in simplest radical
form.
Rationalize the denominator.
Example 5
Find the values of x and y. Give your answers in simplest
radical form.
22 = 2x
Hypotenuse = 2(shorter leg)
11 = x
Divide both sides by 2.
Substitute 11 for x.
Example 6
Find the values of x and y. Give your answers in
simplest radical form.
y = 2(5)
y = 10
Simplify.
Example 7
Find the values of x and y. Give your answers in simplest radical
form.
Rationalize the denominator.
y = 2x
Hypotenuse = 2(shorter leg).
Simplify.
Example 8
sin A =
cos A =
tan A =
opposite
hypotenuse
adjacent
hypotenuse
opposite
adjacent
=
=
=
12
37
35
37
12
35
Example 9
Write a trigonometric ratio.
Substitute the given values.
Multiply both sides by BC and divide by tan 18°.
BC  36.93 ft
Simplify the expression.
Example 10
Write a trigonometric ratio.
Substitute the given values.
JL = 13.6(sin 27°)
JL  6.17 cm
Multiply both sides by 13.6.
Simplify the expression.
Example 11
Find the measure of R and T
Example 12
Classify each angle as an angle of elevation or angle of depression.
1. 6
angle of depression
2. 9
angle of elevation
Example 13
A plane is flying at an altitude of 14,500 ft. The angle of depression from
the plane to a control tower is 15°. What is the horizontal distance
from the plane to the tower?
Example 14
A woman is standing 12 ft from a sculpture. The angle of elevation from her eye to
the top of the sculpture is 30°, and the angle of depression to its base is 22°.
How tall is the sculpture to the nearest foot?