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Question:A 55 meter lighthouse spots a distress signal from a sailboat 143 meters from the base of the lighthouse. What is the angle of depression, to the nearest degree, from the lighthouse to the sailboat?
Answers:I'll draw a picture:
So there's the triangle and we're looking for the angle at the very top.
Now what trig expression has opposite and adjacent sides to it? Tangent does:
Tan x = 143/55
Take the inverse tangent of 143/55 while making sure your calculator is in degrees:
x = 68.96 <===answer
Question:An airplane over the Pacific sights an atoll at a 23 degree angle of depression. If the plane is 445m above water, how many kilometers is it from 445m above the atoll?
Answers:d = 445/tan(23)
d = 1048 km
Question:Calculate the freezing point depression of a benzene solution containing 400g of benzene and 200g of the molecular compound acetone (C9H6O). K(f) for benzene is 5.12 degrees C/m.
Answers:Well I'm pretty sure your formula is wrong. Acetone is the common name for the compound Propanone which has the condensed formula CH3COCH3. As you can see that would be C3H6O not C9H6O.
200 g acetone x 1.00 mol acetone/58.0 g acetone=3.45 mol acetone
3.45 mol/400 g=x/1000 g
So the molality is 8.63 m
8.63 m x 5.12 C/1 m=44.2 C
Question:From the surface of the ocean a diver spots a wooden chest on the ocean floor at an angle of depression of 67 degrees. after she descends 5 meters below the surface, the angle of depression to the chest is 48 degrees. how deep is the ocean where the treasure chest lies? please explain how to do this
Answers:You've been given two triangles.
At the start, the hypotenuse is the distance to the chest. The outside top angle is the angle of depression, so the inside top angle is 90 - that angle, and the height of that side is the height above the floor the diver starts at, and the length of the other side is the horizontal distance away the chest is.
After she descends, the hypotenuse is still the distance to the chest. The outside top angle is still the angle of depression, so the inside top angle is 90 - that angle, and the height of that side is the height above the floor the diver is (so the height they started at minus 5 metres), and the length of the other side is the horizontal distance away the chest is.
So what you have is:
tan(90 - 67) = distance of chest / original depth of diver
tan(90 - 48) = distance of chest / (original depth of diver - 5)
tan23 * original depth of diver = distance of chest
tan42 * (original depth of diver - 5) = distance of chest
tan23 * x = tan42 * (x - 5)
x tan23 = x tan42 - 5 tan42
5 tan42 = x tan42 - x tan23
x (tan42 - tan23) = 5 tan42
x = 5 tan42 / (tan42 - tan23)
x = 9.459...
The diver started at 9.459... metres, which was the surface, so the treasure chest lies at a depth of 9.459... metres
360 degree depression angle over Cheung Chau :360 degree depression angle over Cheung Chau
Angles :Here it is... yes the gig you've all been waiting for subconciously... not featuring Robbie Williams with his never heard before, bonus track, 'Angles' the next in the maths song series now online. Many thanks to 'DJ Hannah' for the music editing... If you fancy another sing song yet again the lyrics are as follows: I calculate, that an angle contemplates its shape but do they know the cases where they show angles we dont know cos Ive been told education lets the mind grow old so when Im sitting in a test Sohcahtoa running through my head and I dont know whats ahead Im loving angles instead and through it all I flick straight to that question the working, is clear perfection whether its right or wrong and written on the wall in bold trigonometry I know that Sin wont fail me when Im out the hall, theyll celebrate me - Im loving angles instead My algebra is weak But I will not just accept defeat I look above on the ceiling maths is still looked upon and as it starts to snow shielding maths books in my clothes and I dont know whats ahead Im loving angles instead and through it all I flick straight to that question the working, is clear perfection whether its right or wrong and written on the wall in bold trigonometry I know that Sin wont fail me when Im out the hall, theyll celebrate me Im loving angles instead