{"id":261744,"date":"2022-09-10T12:42:02","date_gmt":"2022-09-10T07:12:02","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/the-moon-is-observed-from-two-diametrically-opposite-points-a-and-b-on-the-earth-the-angle-%ce%b8-subtended-at-the-moon-by-the-two-directions-of-observation-is-1%e2%88%9854-he\/"},"modified":"2022-09-10T12:42:02","modified_gmt":"2022-09-10T07:12:02","slug":"the-moon-is-observed-from-two-diametrically-opposite-points-a-and-b-on-the-earth-the-angle-%ce%b8-subtended-at-the-moon-by-the-two-directions-of-observation-is-1%e2%88%9854-he","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/physics\/the-moon-is-observed-from-two-diametrically-opposite-points\/","title":{"rendered":"The moon is observed from two diametrically opposite points A and B on the earth. The angle\u00a0\u03b8\u00a0subtended at the moon by the two directions of observation is\u00a01\u221854′.\u00a0he distance of the moon from the earth is [Given diameter of earth\u00a0=1.276\u00d7107\u2009\u2009m]"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"The moon is observed from two diametrically opposite points A and B on the earth. The angle\u00a0\u03b8\u00a0subtended at the moon by the two directions of observation is\u00a01\u221854'.\u00a0he distance of the moon from the earth is [Given diameter of earth\u00a0=1.276\u00d7107\u2009\u2009m]","custom_permalink":"question\/physics\/the-moon-is-observed-from-two-diametrically-opposite-points\/"},"categories":[],"acf":{"question":"

The moon is observed from two diametrically opposite points A and B on the earth. The angle \u03b8<\/mi><\/math> subtended at the moon by the two directions of observation is 1<\/mn>\u2218<\/mo><\/msup>54<\/mn>'<\/mo>.<\/mo><\/math> he distance of the moon from the earth is <\/strong>[Given diameter of earth =<\/mo>1.276<\/mn>\u00d7<\/mo>10<\/mn>7<\/mn><\/msup>\u2009\u2009<\/mtext>m<\/mi>]<\/mo><\/math><\/p>","options":[{"option":"

3.84<\/mn>\u00d7<\/mo>10<\/mn>8<\/mn><\/msup>\u2009\u2009<\/mtext>m<\/mi><\/math><\/p>","correct":true},{"option":"

1.5<\/mn>\u00d7<\/mo>10<\/mn>3<\/mn><\/msup>\u2009\u2009<\/mtext>m<\/mi><\/math><\/p>","correct":false},{"option":"

2.81<\/mn>\u00d7<\/mo>10<\/mn>4<\/mn><\/msup>\u2009\u2009<\/mtext>m<\/mi><\/math><\/p>","correct":false},{"option":"

3.2<\/mn>\u00d7<\/mo>10<\/mn>5<\/mn><\/msup>\u2009\u2009<\/mtext>m<\/mi><\/math><\/p>","correct":false}],"solution":"

Given,<\/span><\/p>

1<\/mn>\u2218<\/mo><\/msup>54<\/mn>'<\/mo>=<\/mo>114<\/mn>'<\/mo>=<\/mo>(<\/mo>114<\/mn>\u00d7<\/mo>60<\/mn>)<\/mo><\/mrow>'<\/mo>'<\/mo>\u00d7<\/mo>(<\/mo>4.85<\/mn>\u00d7<\/mo>10<\/mn>\u2212<\/mo>6<\/mn><\/mrow><\/msup>)<\/mo><\/mrow>r<\/mi>a<\/mi>d<\/mi><\/math><\/p>

=<\/mo>3.32<\/mn>\u00d7<\/mo>10<\/mn>\u2212<\/mo>2<\/mn><\/mrow><\/msup>\u2009\u2009<\/mtext>r<\/mi>a<\/mi>d<\/mi><\/math><\/p>

Since, <\/span>1<\/mn>'<\/mo>'<\/mo>=<\/mo>4.85<\/mn>\u00d7<\/mo>10<\/mn>\u2212<\/mo>6<\/mn><\/mrow><\/msup>\u2009\u2009<\/mtext>r<\/mi>a<\/mi>d<\/mi><\/math><\/p>

Also, <\/span>A<\/mi>B<\/mi>=<\/mo>b<\/mi>=<\/mo>1.276<\/mn>\u00d7<\/mo>10<\/mn>7<\/mn><\/msup>\u2009<\/mtext>m<\/mi><\/math><\/p>

D<\/mi>=<\/mo>b<\/mi>\u03b8<\/mi><\/mfrac><\/math><\/p>

D<\/mi>=<\/mo>1.276<\/mn>\u00d7<\/mo>10<\/mn>7<\/mn><\/msup><\/mrow>3.32<\/mn>\u00d7<\/mo>10<\/mn>\u2212<\/mo>2<\/mn><\/mrow><\/msup><\/mrow><\/mfrac>=<\/mo>3.84<\/mn>\u00d7<\/mo>10<\/mn>8<\/mn><\/msup>\u2009\u2009<\/mtext>m<\/mi><\/math><\/p>

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