Download Examples – Right Triangle Trigonometry

Lesson 26 - Review of Right Triangle
Trigonometry
PreCalculus – Santowski
PreCalculus - Santowski
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(A) Review of Right Triangle Trig
Trigonometry is the study and solution of Triangles.
Solving a triangle means finding the value of each of
its sides and angles. The following terminology and
tactics will be important in the solving of triangles.
 Pythagorean Theorem (a2+b2=c2). Only for right
angle triangles
 Sine (sin), Cosecant (csc or 1/sin)
 Cosine (cos), Secant (sec or 1/cos)
 Tangent (tan), Cotangent (cot or 1/tan)
 Right/Oblique triangle
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(A) Review of Right Triangle Trig
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In a right triangle, the primary trigonometric ratios (which relate pairs of sides
in a ratio to a given reference angle) are as follows:
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sine A = opposite side/hypotenuse side & the cosecant A = cscA = h/o
cosine A = adjacent side/hypotenuse side & the secant A = secA = h/a
tangent A = adjacent side/opposite side & the cotangent A = cotA = a/o
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recall SOHCAHTOA as a way of remembering the trig. ratio and its
corresponding sides
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(B) Review of Trig Ratios
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Evaluate and
interpret:
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Evaluate and
interpret:
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(a) sin(32°)
(b) cos(69°)
(c) tan(10°)
(d) csc(78°)
(e) sec(13°)
(f) cot(86°)
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(a) sin(x) = 0.4598
(b) cos(x) = 0.7854
(c) tan(x) = 1.432
(d) csc(x) = 1.132
(e) sec(x) = 1.125
(f) cot(x) = 0.2768
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(C) Review of Trig Ratios and
Triangles
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(C) Review of Trig Ratios and
Triangles
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(B) Examples – Right Triangle Trigonometry
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Using the right triangle trig ratios, we can solve for
unknown sides and angles:
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ex 1. Find a in ABC if b = 2.8, C = 90°, and A = 35°
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ex 2. Find A in ABC if c = 4.5 and a = 3.5 and B =
90°
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ex 3. Solve ABC if b = 4, a = 1.5 and B = 90°
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(B) Review of Trig Ratios
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If sin(x) = 2/3, determine the values of cos(x) & tan(x)
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If cos(x) = 5/13, determine the value of sin(x) + tan(x)
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If tan(x) = 5/8, determine the sum of sin(x) + 2cos(x)
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If tan(x) = 5/9, determine the value of sin2(x) + cos2(x)
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A right triangle with angle α = 30◦ has an adjacent side X
units long. Determine the lengths of the hypotenuse and
side opposite α.
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Examples – Right Triangle Trigonometry
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Examples – Right Triangle Trigonometry
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(E) Examples – Right Triangle Trigonometry
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A support cable runs from the top of the telephone pole
to a point on the ground 43 feet from its base. If the
cable makes an angle of 32.98º with the ground, find
(rounding to the nearest tenth of a foot):
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a. the height of the pole
b. the length of the cable
A
POLE
mABC = 32 .9 8
B
43 FEET
PreCalculus - Santowski
C
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(E) Examples – Right Triangle Trigonometry
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Mr Santowski stands on
the top of his apartment
building (as part of his
super-hero duties, you
know) and views a villain
at a 29º angle of
depression. If the building
I stand upon is 200 m tall,
how far is the villain from
the foot of the building?
A
E
ANGLE OF DEPRESSION= 29
BUILDING
mADB = 29
C
PreCalculus - Santowski
B
D
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(E) Examples – Right Triangle Trigonometry

You are hiking along a
river and see a tall tree
on the opposite bank.
You measure the angle
of elevation of the top of
the tree and find it to be
46.0º. You then walk 50
feet directly away from
the tree and measure the
angle of elevation. If the
second measurement is
29º, how tall is the tree?
Round your answer to
the nearest foot.
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A
TREE
mABC = 46
C
PreCalculus - Santowski
mADB = 29
B
D
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Examples – Right Triangle Trigonometry
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Examples – Right Triangle Trigonometry
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Examples – Right Triangle Trigonometry
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Examples – Right Triangle Trigonometry
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Examples – Right Triangle Trigonometry
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Examples – Right Triangle Trigonometry
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Examples – Right Triangle Trigonometry
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(8) While driving towards a mountain, Mr S
notices that the angle of elevation to the peak
is 3.5º. He continues to drive to the
mountain and 13 miles later, his second
sighting of the mountain top is 9º.
Determine the height of the mountain.
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