A. Find the height of the mountain; B. Find the distance to the nearest kilometre stone

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From the top of a mountain, in the same vertical plane is two consecutive kilometers stones on the level piece of ground the angles of depression to the kilometer stones are 42° 12 minutes and 23° 30 minutes respectively.



A. Calculate the hate of the mountain
B. Calculate the distance to the nearest kilometre stone




trigonometry




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  • "height" not hate.
    – David Diaz
    Jul 20 at 16:02














up vote
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down vote

favorite












From the top of a mountain, in the same vertical plane is two consecutive kilometers stones on the level piece of ground the angles of depression to the kilometer stones are 42° 12 minutes and 23° 30 minutes respectively.



A. Calculate the hate of the mountain
B. Calculate the distance to the nearest kilometre stone




trigonometry




share|cite|improve this question



















  • "height" not hate.
    – David Diaz
    Jul 20 at 16:02












up vote
0
down vote

favorite









up vote
0
down vote

favorite











From the top of a mountain, in the same vertical plane is two consecutive kilometers stones on the level piece of ground the angles of depression to the kilometer stones are 42° 12 minutes and 23° 30 minutes respectively.



A. Calculate the hate of the mountain
B. Calculate the distance to the nearest kilometre stone




trigonometry




share|cite|improve this question











From the top of a mountain, in the same vertical plane is two consecutive kilometers stones on the level piece of ground the angles of depression to the kilometer stones are 42° 12 minutes and 23° 30 minutes respectively.



A. Calculate the hate of the mountain
B. Calculate the distance to the nearest kilometre stone





trigonometry





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 20 at 15:58









Naftali PNA Shikongo

11




11











  • "height" not hate.
    – David Diaz
    Jul 20 at 16:02
















  • "height" not hate.
    – David Diaz
    Jul 20 at 16:02















"height" not hate.
– David Diaz
Jul 20 at 16:02




"height" not hate.
– David Diaz
Jul 20 at 16:02










1 Answer
1






active

oldest

votes

















up vote
0
down vote













Denote $alpha = 42^circ12'$, $beta = 23^circ30'$.

$h - $ height; $d - $ distance to nearest km stone.



Then
$$tan alpha = dfrachd; tag1$$
$$tan beta = dfrachd+1. tag2$$
So :
$$
dfractanalphatanbeta = dfrach/dh/(d+1)=dfracd+1d =1+dfrac1d.
$$



And therefore
$$
d = dfrac1dfractanalphatanbeta - 1=dfractanbetatanalpha-tanbeta.tag3
$$



Then $h$ can be found easily from $(1), (3)$.






share|cite|improve this answer

















  • 1




    Thank you very much Oleg
    – Naftali PNA Shikongo
    Jul 21 at 16:51










  • @NaftaliPNAShikongo If Oleg's answer was helpful, please upvote or accept it by clicking the up arrow or the checkmark, respectively, near the upper-left corner of the answer.
    – Robert Howard
    Aug 10 at 19:48










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
0
down vote













Denote $alpha = 42^circ12'$, $beta = 23^circ30'$.

$h - $ height; $d - $ distance to nearest km stone.



Then
$$tan alpha = dfrachd; tag1$$
$$tan beta = dfrachd+1. tag2$$
So :
$$
dfractanalphatanbeta = dfrach/dh/(d+1)=dfracd+1d =1+dfrac1d.
$$



And therefore
$$
d = dfrac1dfractanalphatanbeta - 1=dfractanbetatanalpha-tanbeta.tag3
$$



Then $h$ can be found easily from $(1), (3)$.






share|cite|improve this answer

















  • 1




    Thank you very much Oleg
    – Naftali PNA Shikongo
    Jul 21 at 16:51










  • @NaftaliPNAShikongo If Oleg's answer was helpful, please upvote or accept it by clicking the up arrow or the checkmark, respectively, near the upper-left corner of the answer.
    – Robert Howard
    Aug 10 at 19:48














up vote
0
down vote













Denote $alpha = 42^circ12'$, $beta = 23^circ30'$.

$h - $ height; $d - $ distance to nearest km stone.



Then
$$tan alpha = dfrachd; tag1$$
$$tan beta = dfrachd+1. tag2$$
So :
$$
dfractanalphatanbeta = dfrach/dh/(d+1)=dfracd+1d =1+dfrac1d.
$$



And therefore
$$
d = dfrac1dfractanalphatanbeta - 1=dfractanbetatanalpha-tanbeta.tag3
$$



Then $h$ can be found easily from $(1), (3)$.






share|cite|improve this answer

















  • 1




    Thank you very much Oleg
    – Naftali PNA Shikongo
    Jul 21 at 16:51










  • @NaftaliPNAShikongo If Oleg's answer was helpful, please upvote or accept it by clicking the up arrow or the checkmark, respectively, near the upper-left corner of the answer.
    – Robert Howard
    Aug 10 at 19:48












up vote
0
down vote










up vote
0
down vote









Denote $alpha = 42^circ12'$, $beta = 23^circ30'$.

$h - $ height; $d - $ distance to nearest km stone.



Then
$$tan alpha = dfrachd; tag1$$
$$tan beta = dfrachd+1. tag2$$
So :
$$
dfractanalphatanbeta = dfrach/dh/(d+1)=dfracd+1d =1+dfrac1d.
$$



And therefore
$$
d = dfrac1dfractanalphatanbeta - 1=dfractanbetatanalpha-tanbeta.tag3
$$



Then $h$ can be found easily from $(1), (3)$.






share|cite|improve this answer













Denote $alpha = 42^circ12'$, $beta = 23^circ30'$.

$h - $ height; $d - $ distance to nearest km stone.



Then
$$tan alpha = dfrachd; tag1$$
$$tan beta = dfrachd+1. tag2$$
So :
$$
dfractanalphatanbeta = dfrach/dh/(d+1)=dfracd+1d =1+dfrac1d.
$$



And therefore
$$
d = dfrac1dfractanalphatanbeta - 1=dfractanbetatanalpha-tanbeta.tag3
$$



Then $h$ can be found easily from $(1), (3)$.







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered Jul 20 at 16:08









Oleg567

13.6k22969




13.6k22969







  • 1




    Thank you very much Oleg
    – Naftali PNA Shikongo
    Jul 21 at 16:51










  • @NaftaliPNAShikongo If Oleg's answer was helpful, please upvote or accept it by clicking the up arrow or the checkmark, respectively, near the upper-left corner of the answer.
    – Robert Howard
    Aug 10 at 19:48












  • 1




    Thank you very much Oleg
    – Naftali PNA Shikongo
    Jul 21 at 16:51










  • @NaftaliPNAShikongo If Oleg's answer was helpful, please upvote or accept it by clicking the up arrow or the checkmark, respectively, near the upper-left corner of the answer.
    – Robert Howard
    Aug 10 at 19:48







1




1




Thank you very much Oleg
– Naftali PNA Shikongo
Jul 21 at 16:51




Thank you very much Oleg
– Naftali PNA Shikongo
Jul 21 at 16:51












@NaftaliPNAShikongo If Oleg's answer was helpful, please upvote or accept it by clicking the up arrow or the checkmark, respectively, near the upper-left corner of the answer.
– Robert Howard
Aug 10 at 19:48




@NaftaliPNAShikongo If Oleg's answer was helpful, please upvote or accept it by clicking the up arrow or the checkmark, respectively, near the upper-left corner of the answer.
– Robert Howard
Aug 10 at 19:48












 

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