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Trigonometry (MindTap Course List)

8th Edition
Charles P. McKeague + 1 other
ISBN: 9781305652224
Textbook Problem

Problems 45 and 46 refer to Figure 10, which is a diagram of the Colnago Dream Plus bike ‘frame. The frame can be approximated as two triangles that have the seal tube as a common side.

Bike Frame Geometry The 50-centimeter Colnago frame has a top tube length of 52.3 centimeters, a seat tube length of 48.0 centimeters. and a seat angle of 75.0°. Find the length of the down tube and the angle between the seat tube and the down tube.

To determine

To calculate:

The length of the down tube and the angle between the seat tube and the down tube.

Explanation

Given information:

Length of the top tube =52.3cm

Seat tube length =48.0cm

Seat angle =75°

Formula used:

The cosine rule is b2=a2+c22accosB.

Calculation:

The triangle is:

To find the value of b, use the cosine rule.

b2=a2+c22accosB=(48)2+(52.3)22(48)(52.3)cos(75)=2304+2735.295020.8(0.2588)=2304+2735.291299.38=3739.9

Take square root on both sides.

b2=3739

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