Download Sec. 5.1 Trigonometric Ratios of Acute Angles

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Sec. 5.1 Trigonometric Ratios of Acute Angles
Review of Skills from Grade 10
A) Pythagorean Theorem ­ for Right Triangles Only
hypotenuse
(hypotenuse)2 = sum of the squares of the other two sides
Example # 1: Find the length of the missing side.
15 m
a)
b)
y x
12 cm
25 m
5 cm
B) Primary Trigonometric Ratios ­ for Right Triangles Only
hypotenuse
hypotenuse
opposite
adjacent
adjacent
opposite
The three primary trigonometric ratios are sine (sin), cosine (cos) and tangent (tan). The acronym we use to help us remember the relationship between the sides of the right triangle and the angle is "SOH CAH TOA"
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Example # 2: State the primary triognometric ratios for angle D.
8 mm
adjacent
8 mm
17 mm
17 mm
opposite
hypotenuse
Reciprocal Trigonometric Ratios
Just like there are 3 primary trigonometric ratios, there is also 3 reciprocal trigonometric ratios. They are cosecant (csc), secant (sec) and cotangent (cot).
Example # 3: Evaluating the six trigonometric ratios of an angle.
Triangle XYZ is a right triangle with side lengths of 10 cm , 24 cm and 26 cm. If
YZ = 10 cm and angle Z is 900, which trigonometric ratio of angle Y is the
greatest?
Example # 4: Solving for a side or angle in a right triangle.
a)
John is lying on the ground, 3.7 m b)
from the base of a tree. He
measures the angle of inclination to
the top of the tree to be 650 using a
clinometer. How tall is the tree,
to the nearest tenth of a meter?
A wheelchair ramp rises 8" for every
1 foot of horizontal distance. A
wheel chair ramp into a new house
needs to be built. The door is 4 feet
above ground level. What angle of
elevation should the ramp be
constructed at to maintain the
proper proportions?
Therefore the height of the tree is approximately 7.9 m tall.
Therefore the ramp should be constructed with an angle of elevation of 33.7o
Homework p. 280 # 1-4 , 5ab (i,iii) , 6ac , 7a , 8b , 11 , 12
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