Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 70, Problem 15A

Find length x.
All dimensions are in millimetersChapter 70, Problem 15A, Find length x. All dimensions are in millimeters

Expert Solution & Answer
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To determine

The length x.

Answer to Problem 15A

The length x is 299.45mm.

Explanation of Solution

Given information:

The below diagram represents the given section.

  Mathematics For Machine Technology, Chapter 70, Problem 15A

       Figure -(1)

Write the expression for sinθ from triangle GHT.

sinGHT=GHGT   ...... (I)

Here, height of triangle GHT is GH and hypotenuse of triangle GHT is GT.

Write the expression for tanGHT from triangle GHT.

tanGHT=GHHT   ...... (II)

Here, height of triangle GHT is GH and hypotenuse of triangle GHT is GT.

Write the expression for length BC.

BC=MC(tanBCM)   ...... (III)

Here, length between points M and C is MC and angle C of triangle BCM is BCM.

Write the expression for length AB.

AB=EP(sinABP)   ...... (IV)

Here, length between points E and P is EP and angle B of triangle ABP is ABP.

Write the expression for length x using the geometry.

x=AB+BC+CD+DE+EF   ...... (V)

Here, distance between points C and D is CD, distance between points D and E is DE and distance between points E and F is EF.

Write the expression for length GH.

GH=GDHD   ...... (VI)

Calculation:

Subsitute 80mm for GD and 37.5mm for HD in Equation (VI).

GH=80mm37.5mm=42.5mm

Write the length GT from the geometry.

GT=41.70mm+36.80mm=78.5mm

Substitute 42.5mm for GH and 78.5mm for GT in Equation (I).

sinGHT=( 42.5mm)( 78.5mm)GHT=sin1( 42.5mm 78.5mm)GHT=32.78°

Substitute 32.78° for GHT and 42.5mm for GH in Equation (II).

tan32.78°=42.5mmHTHT=tan32.78°×42.5mmHT=66mm

The legth of HT and DE are same.

DE=66mm

Substitute 80.50° for BCM and 80mm for MC in Equation (III).

BC=80mm( tan80.50°)=5.97=13.38mm

Substitute 80.50° for ABP and 70mm for EP in Equation (IV).

AB=70mm( sin80.50°)=70mm( 0.9862)=70.97mm

The length CD and MG are same.

Write the length CD from the geometry.

CD=70mm+41.70mm=111.7mm

Substitute 70.97mm for AB, 13.98mm for BC, 111.7mm for CD, 66mm for DE

36.8mm for EF in Equation (V).

x=70.97mm+13.98mm+111.7mm+66mm+36.8mm=84.95mm+214.5mm=299.45mm

Conclusion:

The length x is 299.45mm.

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Chapter 70 Solutions

Mathematics For Machine Technology

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