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Applications
of Trigonometry |
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Right-angled
Triangle or Right Triangle |
Trigonometric functions of an acute angle defined in a right triangle
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Solving right triangles |
Solving right triangles
examples |
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Right-angled
Triangle
or Right Triangle |
Trigonometric functions of an acute angle defined in a right triangle
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Trigonometric
functions of an acute angle are defined in a right triangle as a
ratio of its sides. |
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Solving
the right triangle |
To
solve a right triangle means to find all unknown sides and
angles using its known parts. |
While
solving a right triangle we use Pythagoras’
theorem and trigonometric functions
of an acute angle depending
which pair of its parts is given |
Note,
right triangles are usually denoted as follows; c
stands for the hypotenuse, a
and b
for the perpendicular
sides called legs, and a
and b
for the angles opposite to a
and b
respectively. |
There
are four basic cases that can occur, given |
a)
hypotenuse and angle, c)
hypotenuse and leg, |
b)
leg and angle,
d) two legs. |
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Solving right triangles examples |
Example:
Which highest level h will reach a bob pendulum of length
l, starting from rest, where
j is the largest angle attained by the pendulum. |
Solution: Given
l and
j.
h
= ? |
From the right triangle in
the right figure |
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Example:
In an isosceles triangle two equal sides subtend angles
a
at the endpoints of the third side. |
What is the length of the third side if the difference between the altitude of the triangle to that side, and the radius of the inscribed circle, equals
d? |
Solution: Given
a and
d.
a = ? |
angle
ESC
= angle
EAD
= a
- the angles with mutually perpendicular sides |
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Example:
From a distance an observer sees the top of a church tower at the angle of elevation a = 18°9′34″
when comes 100 m closer, under the angle
b
= 28°39′50″. Find the height
h
of the church and
the distance x. |
Solution: From the
two right triangles |
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Example:
Find the angle a
between a lateral edge and the base, and the base-to-face dihedral angle
b of the regular tetrahedron shown in
the figure below. |
Solution: R -the radius of circumscribed circle,
r
-the radius of inscribed circle, h
-height of the tetrahedron and ha -height of a face
(the equilateral triangle). |
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Geometry
and use of trigonometry contents - B |
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