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Chapter 8: Q. 38 (page 528)

Distance to the Moon At exactly the same time, Tom and Alice measured the angle of elevation to the moon while standing exactly 300 km apart. The angle of elevation to

the moon for Tom was 49.8974掳 and the angle of elevation to the moon for Alice was 49.9312掳. See the figure. To the nearest 1000 km, how far was the moon from Earth when

the measurement was obtained?

Short Answer

Expert verified

The average distance between moon and earth is approximately 389076.76 km.

Step by step solution

01

Step 1. Given Information

In the diagram, let the vertex representing Tom be T, Alice be A and Moon be M.

Then the distance between Tom and Alice is m=300, the distance between moon and Alice be tand the distance between moon and Tom bea.

02

Step 2. Finding the angles

Find angle M using the linearly opposite angles in triangle, therefore

M=49.9312-49.8974M=0.0338慰

Find angle A using the property of supplementary angles, therefore

A=180-49.9312A=130.0688慰

03

Step 3. Finding distance Tom and moon

asinA=msinMa=sin130.0688慰脳300sin0.0338慰a=389173.32

04

Step 4. Finding distance between moon and Alice

tsinT=msinMt=sinT脳msinMt=sin49.8974慰脳300sin0.0338慰t=388980.14

05

Step 5. Finding close approximation of the distance between earth and moon

d=388980.14+389173.322=389076.73

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