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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
asked Jul 20 at 15:58
Naftali PNA Shikongo
11
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up vote
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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
asked Jul 20 at 15:58
Naftali PNA Shikongo
11
"height" not hate.
– David Diaz
Jul 20 at 16:02
add a comment |Â
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
asked Jul 20 at 15:58
Naftali PNA Shikongo
11
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
asked Jul 20 at 15:58
Naftali PNA Shikongo
11
asked Jul 20 at 15:58
Naftali PNA Shikongo
11
asked Jul 20 at 15:58
Naftali PNA Shikongo
11
asked Jul 20 at 15:58
Naftali PNA Shikongo
11
11
"height" not hate.
– David Diaz
Jul 20 at 16:02
add a comment |Â
"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
add a comment |Â
1 Answer
1
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oldest
votes
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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 $(1), (3)$.
answered Jul 20 at 16:08
Oleg567
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
add a comment |Â
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 $(1), (3)$.
answered Jul 20 at 16:08
Oleg567
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
add a comment |Â
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 $(1), (3)$.
answered Jul 20 at 16:08
Oleg567
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
add a comment |Â
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 $(1), (3)$.
answered Jul 20 at 16:08
Oleg567
13.6k22969
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 $(1), (3)$.
answered Jul 20 at 16:08
Oleg567
13.6k22969
answered Jul 20 at 16:08
Oleg567
13.6k22969
answered Jul 20 at 16:08
Oleg567
13.6k22969
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
add a comment |Â
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
add a comment |Â
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"height" not hate.
– David Diaz
Jul 20 at 16:02