Download Alg. II 13-1 An Introduction to Trigonometry

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Alg. II
13-1 An Introduction to Trigonometry
Trigonometry can be used to find the missing measures of
triangles. Refer to the diagram at the right.
The hypotenuse of triangle ABC is side AB,
and its length is c units. The side opposite
angle A is side BC. Its length is a units.
The side adjacent to angle A is side AC.
Its length is b units.
sin A =
cos A =
tanA =
csc A =
sec A =
cot A =
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Suppose A is an acute angle of a right triangle.
For each function find the values of the
remaining 5 trig functions of A. Write in radical
form and round to four decimals.
1. Sin A = 3/2
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30-60-90 triangle formulas
hyp = 2Ls
LL = 3 Ls
Find all the trig functions for a 30-60-90 triangle
45-45-90 triangle formulas
Legs are equal
Hyp = 2 leg
Find all the trig functions for a 45-45-90 triangle
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Find the value of x. Leave in radical form.
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13-1 Day 2
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5. A 150-foot rope is tied from the top of a
100-foot-tall pole to a stake in the ground. What is
the angle between the rope and the ground?
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6. A 6-foot-long pipe is propped on a 3-foot-tall
packing crate that sits on level ground. One foot of
the pipe extends above the top edge of the crate
and the other end rests on the ground.
What angle does the pipe form with the ground?
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7. A car is traveling 750 meters along a ramp raised
4 degrees from the ground. How far did it rise
during this distance?
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Angle of elevation and angle of depression.
8. Trevor is standing on top of a cliff 200 feet
above a lake. The measurement of the angle of
depression to a boat on the lake is 21 degrees. How
far is the boat from the base of the cliff to the
nearest foot?
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9. A geologist measured a 43 degree angle of
elevation to the top of a volcano crater. After
moving .25 km farther away, the angle of elevation
was 38 degrees. How high is the top of the volcano
crater?
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