Question 1040554
Let {{{ h }}} = the height of the building
Let {{{ d }}} = distance in the 1st case from
surveyor to base of building
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(1) {{{ tan( 28.5 ) = h/d }}}
(2) {{{ tan( 32.5 ) = h/( d - 100 ) }}}
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(1) {{{ .54296 = h/d }}}
(2) {{{ .63707 = h/( d - 100 ) }}}
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(1) {{{ h = .54296d }}}
(2) {{{ h = .63707*( d - 100 ) }}}
Substitute (1) into (2)
(2) {{{ .54296d = .63707d - 63.707 }}}
(2) {{{ .09411d = 63.707 }}}
(2) {{{ d = 676.94 }}}
and
(1) {{{ h = .54296d }}}
(1) {{{ h = .54296*676.94 }}}
(1) {{{ h = 367.55 }}}
The height is 368 ft to the nearest foot
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check answer:
(1) {{{ .54296 = h/d }}}
(1) {{{ .54296 = 367.55 / 676.94 }}}
(1) {{{ .54296 = .54296 }}}
and
(2) {{{ .63707 = h/( d - 100 ) }}}
(2) {{{ .63707 = 367.55/( 676.94 - 100 ) }}}
(2) {{{ .63707 = 367.55 / 576.94 }}}
(2) {{{ .63707 = .63707 }}}
OK