2.5 - more right triangle word problems -...

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2.5 - More Right Triangle Word Problems

In Navigation, they give angles in BEARINGS.

A plane flies 200 miles with a Bearing of 70o

Bearing: TYPE 1

BEARING ( aka heading or course ):***The angle is measured from the North going clockwise

N

EW

70 o200 mi

S

2

Bearing 120 o Bearing 300 o

Bearing 24 oBearing 215 o

Bearing 95 oBearing 190o

N

S

EW

N

S

EW

N

S

EW

N

S

EW

N

S

EW

N

S

EW

Bearing: TYPE 2 ***The angle is sandwiched between to directions

A boat is traveling 50 mph for 3 hrs on a bearing of S 20o E.

150 miles

N

S

EW

20 o

150 mi

From the South turn 20o to the East

3

N 25o W N 50o E

S 80o W S 60o E

Always starts N or S then turns an ACUTE ANGLE E or W

N

W

S

E

N

W

S

E

N

W

S

E

N

W

S

E

It is critical that your drawing is neat, accurate, and labeled!!!

1.) Read the problem.2.) Sketch a diagram.3.) Find and label the RIGHT TRIANGLE.4.) Set up an Equation and solve.5.) Answer the question.

Steps for Story Problems

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The bearing from Atlanta to Macon is S 27o E, and the bearingfrom Macon to Augusta is N 63o E. A car traveling 60 mph

needs 1 1/4 hrs to go from Atlanta to Macon and 1 3/4 hrs to go from Macon to Augusta. Find the distance and

bearing from Atlanta to Augusta.

27o

75

A

63o 105

M

? AugA

M

27o

d = rtd = 60(1.25)d = 75 mi

d = rtd = 60(1.75)d = 105 mi

c 2 = 752 + 1052

c≈129 milesTan A = 105 75

A≈54.5

o

oAnswer : 129 miles with a bearing of S 81.5 o E

54.5 o

5

The angle of elevation to the top of a building is 41o. When you walk 168 ft closer to the building, the angle of elevation is 530. How tall is the building?

41 o

168 + x

h

x53 o

htan 53 = h x

x tan 53 =htan 41 = h x + 168

tan 41 ( x + 168 ) = h

x tan 41 + 168 tan 41 = h

x tan 53 = x tan 41 + 168 tan 41

x tan 53 = x tan 41 + 168 tan 41

x tan 53 - x tan 41 = 168 tan 41

x ( tan 53 - tan 41 ) = 168 tan 41

x = 168 tan 41 ( tan 53 - tan 41 )

6

tan 53 = h xx tan 53 = h

But they asked for the height!

tan 53 =h 168 tan 41 ( tan 53 - tan 41 )

pg. 81: 11, 12, 13, 15, 23, 25