Help with a trig question

[graci]

I have been taught only laws of sines so far so this question has to do with laws of sine -

A rocket 20m long going straight up is being observed from a point on ground 1000m from the launch site. If x is the angle between sightings to the tail and nose of the rocket and h is the height of the rocket above ground write an equation that gives angle x as a function of h.

 

[Deleted member 4993]

I have been taught only laws of sines so far so this question has to do with laws of sine -

A rocket 20m long going straight up is being observed from a point on ground 1000m from the launch site. If x is the angle between sightings to the tail and nose of the rocket and h is the height of the rocket above ground write an equation that gives angle x as a function of h.

If I were to solve your assignment, I would first draw a sketch of the "situation"

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[Dr.Peterson]

I have been taught only laws of sines so far so this question has to do with laws of sine -

A rocket 20m long going straight up is being observed from a point on ground 1000m from the launch site. If x is the angle between sightings to the tail and nose of the rocket and h is the height of the rocket above ground write an equation that gives angle x as a function of h.

Which part of the rocket is h meters above the ground?

Draw a picture with h and x labeled, along with the fixed values.

You don't have to use the law of sines; but if you want to, you'll need to find a second side of the triangle containing angle x, since the law of sines requires two sides and an angle in order to find an angle.

 

[Otis]

this question has to do with laws of sine

Hi graci. To me, the question seems custom-made for the arctangent function. There are two right triangles in the given scenario, and we can write expressions in terms of h for the vertical legs in each.

Either way, can you share your picture?

PS: If I were to guess, I would measure h from the ground to the bottom of the rocket.

?

 

[Otis]

 

[Deleted member 4993]

I have been taught only laws of sines so far so this question has to do with laws of sine -

A rocket 20m long going straight up is being observed from a point on ground 1000m from the launch site. If x is the angle between sightings to the tail and nose of the rocket and h is the height of the rocket above ground write an equation that gives angle x as a function of h.

Assume that the angle of elevation of the tail from the ground is 'y'

What is the expression (equation) for tan(y)?​

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What is the expression (equation) for tan(y+x) - from your sketch?​

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Now expand tan(y+x) - using known trigonometric identities.​

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What is the expression (equation) for tan(x)​