There are many ropes keeping a hot air balloon from floating away before a balloon race. One of these ropes is fixed to the ground at a 45° angle. Another is fixed to the ground at a 30° angle. If the hot air balloon is 18 feet off the ground, what is the distance between the ground directly underneath the balloon and the second rope rounded to the nearest hundredth of a foot?

- anonymous

- katieb

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- anonymous

Use basic trigonometric formulas and you will get the answer.....give it a try

- anonymous

im trying but im so stuck :/

- anonymous

ok so draw the figure and then try ......there is an option down called draw...use it and draw the figure then let me tell u the step by step procedure

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## More answers

- anonymous

Draw a picture, |dw:1326910244892:dw|, then figure out the lengths of the distance between the middle point of the triangle and the second rope (the one at a 30 degree angle). Take the problem one step at a time

- anonymous

|dw:1326910345044:dw|

- anonymous

|dw:1326910115983:dw|

- anonymous

sorta! i can draw in this at all

- anonymous

Balloon 18 feet in air held by two ropes forming two right triangles. Rope 1 forms a base angle of 45 degrees. Rope 2 forms a base angle of 30 degrees.

- anonymous

ok so now how do i find the answer!

- anonymous

use one of the trig ratios sin cos or tan
the second rope refers to the angle 30 degrees i guess

- anonymous

i dont know..thats why i posted this...

- anonymous

you need to find which side is opposite the 30 degrees and which is adjacent- does that help?

- anonymous

so the hypotenuse??????

- anonymous

can you just give me the answer it will save me so much time.,..

- anonymous

no - the hypotenuse is the longest side of the rt angled triangle - in this case its the rope
the opp side is the 18 ft and ground length(which is what you need is adjacent ( to 30 degree angle}
so u need the ration which is opposite / adjacent
which is ??

- anonymous

im not working on those tho!! im working on 45-45-0 and 30-60-90 triangles

- anonymous

ok i can give u the answer - i was also trying to help you with the concept
ok in 30-60-90 triangle, side opposite 30 degrrees is 1 and adjacent is 2
so 1 / 2 = 18 / x
x = 36 - thats the distance you require

- anonymous

oh no - i'm an idiot - sorry opp side is 1 and adjacent is sqrt3
so 1 / sqrt3 = 18 / x
so x = 18*sqrt3

- anonymous

so what is the main answer????

- anonymous

correct is 18*sqrt3 or 31.18 feet to 2 dec places

- anonymous

thanks..

- anonymous

yw

- anonymous

well, i have another wuestion but are you able to answer it in a simpler way?

- anonymous

yea

- anonymous

ok...one second please.

- anonymous

In the figure below, the length of line segment CB is 64 units and the length of line segment BG is 137 units. What is the length of line segment EA?

- anonymous

i will draw it one moment

- anonymous

|dw:1326911563739:dw|

- anonymous

length of BA = BC = 64
so length of AG = 137 - 64 = 73
as angle EAG = 60 degrees AG / EA = 1/2
so 73 / EA = 1/2
EA = 2*73 = 146

- anonymous

so the answer is 146?

- anonymous

yes 146

- anonymous

ok! and i promise this is the last one i have 1 more.

- anonymous

A toddler’s playground has two slides on either side. The slide on the left is situated at a 45° angle to the ground and is 52 centimeters away from the base of the playground. The slide on the right is positioned at a 30° angle to the ground and is 98 centimeters away from the playground’s base. What is the total length of both slides on this playground rounded to the nearest tenth of a centimeter?
Playground with two slides. Left slide has base measuring 52 centimeters and base angle of 45 degrees. Right slide has base measuring 98 centimeters and base angle of 30 degrees.

- anonymous

do you need me to draw this?

- anonymous

no its alright ill draw it

- anonymous

ok i think it is asking for perimeter? im not quite sure though.

- anonymous

|dw:1326912527404:dw|

- anonymous

445.287? i think that is the correct answer

- anonymous

no sorry..i screwed that up im stupid..

- anonymous

no wait..thats correct. i believe.

- anonymous

its asking for the lengths of the slides themselves - the sloping parts

- anonymous

so 165.167?

- anonymous

45 degree slide has length 52sqrt2
30 ................................ 98*2 = 196
total is 269.54

- anonymous

oh....ok

- anonymous

yourmom the first slide measure comes to 52/sin 45 and the next one is 98/sin 30

- anonymous

what we are finding is lengths of hypotenuse

- anonymous

i know that. so one second.

- anonymous

so like jimmyrep says 269.54 is the answer

- anonymous

i put that and got it wrong..thanks..

- anonymous

that was wrong but thanks anyway..

- anonymous

sorry your mom it comes to 263.54

- anonymous

its ok b

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