Question

A surveyor is standing 120 meters from the base of a tower. He determines that the angle of elevation (the angle formed by the ground and the surveyor’s line of sight to the top of the tower) is 30 degrees. The surveyor’s eye level is 1.7 meters above the ground. Find the height of the tower.

Answer 1

theres image i need help understanding

Answer 2

Use law of sines. You should get your tower to be 69.28 meters tall

Answer 3

So we can assume that there is a 90 degree angle between the height and distance away and since triangles have 180 degrees total, you know the other degree of 60 degrees. You know the idea behind 30-60-90 triangles, right?
Alternatively you can use sine.

Answer 4

law of snines?

Answer 5

your setup should be something like 120/sin60 = H/sin30 , where H is the height of your tower

Answer 6

um, tan(30) = x/120

120 tan(30) = x

then add in the 1.7m

Answer 7

ummmmm x=(120 sin 30/cos 30) + 1.7
sin/cos=tan

Answer 8

that works too :)

Answer 9

i still cant solve it

Answer 10

how come? all thats left is to use a calculator or recall the basic 30-60-90 tri that it comes from

Answer 11

hold on a sec let me show you what i got so far

Answer 12

thats not right .....

Answer 13

i dont get it

Answer 14

if you insist on the law of sines; which is way more work than is required ...

x/sin(30) = 120/sin(60)

x = 120 sin(30)/sin(60)

then add in the 1.7

sin(60) = cos(30)

sin(30)/sin(60) = sin(30)/cos(30) = tan(30)

Answer 15

your easiest bet is just:

height = 120 tan(30) + 1.7

Answer 16

so is it 70.982?

Answer 17

looks good. the trick is to make sure your calculator is on degrees :)

http://www.wolframalpha.com/input/?i=120+tan%2830%29+%2B+1.7

Answer 18

oh ok i did have it on radians for some reason

Answer 19

thanks for the help

Answer 20

yep

Answer 21

70.982032302755091741097853660235 ohhh dear