Right triangle problems

Solving Right Triangle Problems

Mathematics 4

October 27, 2011

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Right triangles and the unit circle

Sine, cosine, and the unit circle:

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Right triangles and the unit circle

Right triangles beyond the unit circle:

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Right triangles and the unit circle

We can relate the two righttriangles by similarity:

sin θ

opp=

cos θ

adj=

1

hyp

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Right triangles and the unit circle

We can relate the two righttriangles by similarity:

sin θ

opp=

cos θ

adj=

1

hyp

Isolating the trigonometricfunctions:

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Right triangles and the unit circle

We can relate the two righttriangles by similarity:

sin θ

opp=

cos θ

adj=

1

hyp

Isolating the trigonometricfunctions:

sin θ =opp

hyp

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Right triangles and the unit circle

We can relate the two righttriangles by similarity:

sin θ

opp=

cos θ

adj=

1

hyp

Isolating the trigonometricfunctions:

cos θ =adj

hyp

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Right triangles and the unit circle

We can relate the two righttriangles by similarity:

sin θ

opp=

cos θ

adj=

1

hyp

Isolating the trigonometricfunctions:

tan θ =opp

adj

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Solve the right triangles given the following parts:

1. α = 17o, a = 135

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Solve the right triangles given the following parts:

1. α = 17o, a = 135 β = 73o, c = 461.7, b = 441.6

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Solve the right triangles given the following parts:

1. α = 17o, a = 135 β = 73o, c = 461.7, b = 441.6

2. a = 64.5, b = 57.2

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Solve the right triangles given the following parts:

1. α = 17o, a = 135 β = 73o, c = 461.7, b = 441.6

2. a = 64.5, b = 57.2 α = 48.4o, β = 41.6o, c = 86.2

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Applications of Right Triangle Solutions:

Definition of terms:

Angle of Elevation Angle of Depression

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Applications of Right Triangle Solutions:

Example 1

Find the length of the pole, and the distance of the pole from thebuilding.

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Applications of Right Triangle Solutions:

Example 2

Find the distance across the river (indicated by PQ)

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Applications of Right Triangle Solutions:

Example 3: The problem needs to be illustrated first

How high is a building whose horizontal shadow is 50meters when the angle of elevation of the sun is 65degrees?

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Applications of Right Triangle Solutions:

Example 4

An 18-meter ladder leaning up against a buildingmakes a 70 degree angle with the ground. How far upthe building does the ladder touch?

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Applications of Right Triangle Solutions:

Example 5

A 36-foot ladder is used to reach the top of a 28-footwall. If the ladder extends 2 feet past the top of thewall, find its inclination to the horizontal.

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Applications of Right Triangle Solutions:

Definition of Terms:

Course - angle measured indegrees clockwise from the northto the direction a ship is traveling.

Bearing - angle measured indegrees clockwise from the northof Ship A to the line segmentconnecting Ship A and Ship B.

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Applications of Right Triangle Solutions:

Example 6

Two ships leave a port at the same time. The firstship sails on a course of 25 degrees at 15 knots (1knot = 1 mi/hr) while the second ship sails on acourse of 115 degrees at 20 knots. Find after twohours (a) the distance between the ships, and (b) thebearing from the first ship to the second and (c) thebearing of the second ship to the first.

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Any questions?

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