Step 1 Use pens, pencils, rulers, etc
Step 2 Then draw
Formulate, draw then solve the following scenes:
- A man standing on the beach looks up to the top of the cliff with an angle of elevation of 65 degrees. Ignoring his height and assuming he is standing on level ground with the base of the cliff and he is 15 metres from the base of the cliff, determine the height of the cliff.
- From the question above, if the man walk 5 metres closer to the cliff and looks up to the top of the cliff, what will his angle of elevation be?
- A man standing on the beach looks up to the top of the cliff with an angle of elevation of 70 degrees. Ignoring his height and assuming he is standing on level ground with the base of the cliff and he is 20 metres from the base of the cliff, determine the height of the cliff. A lady on the beach look up to the top of the same cliff with an angle of elevation of 40 degrees. Ignoring her height, determine the distance she stands from the base of the cliff.
solution 1
ReplyDeletesin= opp/hyp , cos= adj/hyp
tan= opp/adj
we use tan= opp/adj
because the lenght from the man to the base of the cliff is 15m; this is the adj. side
the opp.=height(unkown)
angle of elevation= 65
so
tan 65/1 = h/15
h = 15 tan 65
h = 32.17
therefore height is 32.17m
solution 2
ReplyDeletewhen the man walks 5 meters closer to the base of the cliff the adj is decreased by 5.
therefore
tan 0 = opp/adj
tan 0 = 32.17/10
tan 0 = 3.217
0 = tan inverse 3.217
0 = 72.73
so
angle of elevation is 72.73 Degrees
solution 3
ReplyDeletequite similar to others
sin = opp/hyp, cos= adj/hyp
tan = opp/adj
using tan = opp/adj
tan70 /1= h/20
h= 20 tan 70
h= 54.95
so
therefore height of cliff is 54.95 m
part 11
the lady looks up at 40 degrees to a height of 54.95m
so
tan 0 = opp/adj
tan40 /1 = 54.95 /adj
0.84 /1 = 54.95 /adj
54.95 = 0.84 adj
54.95/.84= adj
65.41= adj
therefore the distance from the base of the cliff to where she is standing is 65.41 m
someone review my answers!!
ReplyDeletefirst answer is correct.
ReplyDeletesecond solution is correct
ReplyDeletethe both solutions are coorect,well done...
ReplyDeletewe can't stop there guys one question isn't effort to help us for exam answer my question..........below
ReplyDeleteThe ange between a wall in a building and the rafters is 124 degrees. The line from the ridge of the roof to the bottom of the wall makes an angle of 25 degrees with the wall.
ReplyDeletea) Determine the lenght of the rafters if the wall is 5M high.
b) Determine the height of the wall if the lenght of the rafters is 6.5M high.
REMEMBER :
ReplyDeleteSOHCAHTOA
break it up:
SOH.... sin(X) = opp/hyp
CAH.... cos(x) = adj/hyp
TOA.... tan(x) = opp/adj
solution to question 1:
ReplyDeletefor the triangle i have pictured i needed to find the opposite.
other info i had was the angle of elevation (65 degrees) and the adjacent (15 m)
so we can use:
Tan(x) = opp/adj
where x = angle
=> tan(65) = opp/15
tan(65)(15) = opp
therefore opposite = 32.17 m
solution to question 2:
ReplyDeleteif the man is 5 m closer to the base of the cliff then the adjacent distance will now change to 10 m (15 m - 5 m)
we already have the height of the cliff (32.17 m)...
using the same formula: tan(x) = opp/adj
we say:
tan(x) 32.17/10
tan(x) = 3.217
x = tan inverse (3.217)
i.e : tan^-1 (3.217)
= 72.73 degrees
in this case we had to find the angle since we were already given the opposite and adjacent distances.
solution to question 3:
ReplyDeletefor the man:
tan(x) = opp/adj
tan(70) = opp/20
tan(70)(20) = opp
=> opp = 55 m
for lady:
tan(40) = 55/adj
tan(40)adj = 55
adj = 55/tan(40)
adj = 65.5 m
1. A bird is standing on the ground, 5 metres away from a tree, which is seven metres tall. The bird wants to build a nest at the top of the tree, what is the shortest distance the bird must fly to get from its point on the ground to the top of the tree?
ReplyDelete2. Your friend climbs up a flight of stairs, travelling 10 metres diagonally, when she gets to the top of the stairs she accidentally kicks over your cell phone which you left charging. To make sure your phone isn’t damaged, you need to calculate how far it fell from the top of the stairs straight down to the floor, and you know the stairs are at an angle of 53 degrees.
3. You are 6 metres away from a target with a canon that rests on the ground. The target is 5m off the ground. What angle would the canon need to be at to hit the target?
4. A friend is sleeping on the street across the road from your building, and you are standing on the balcony of the 5th floor. The road is 20m wide, and each floor is 5m high. What angle would your friend need to look up to see you if you called to him?
solution 1
ReplyDeleteIn a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.
So
the square of a a plus the square of b is equal to the square of c :
A squared + B squared = C squared
height of tree = 7 M.
distance from the tree to where the bird is standing is = 5 M.
using pythagoras theorm
A squared + B squared = C squared
7 squared + 5 squared = C squared
49 + 25 = c squared
74 = c squared
square root of 74 = c
8.6 = c
therefore
Distance the bird fly is 8.6 meters
ANSWER = 8.6 METERS
solution 2
ReplyDeletesin = opp / hyp
cos = adj / hyp
tan = opp / adj
from the question
hyp = 10 M
opp = h (unknown)
elvation of the stairs 53 degrees
therefore use sin = opp / hyp
so
sin 53 / 1 = h / 10
h * 1 = 10 sin 53
h = 7.99
answer
the phone fell a distance of: 7.99 M
solution 3
ReplyDeletegiven
adj = 6
opp = 5
angle inclined = x
therefore use tan = opp / adj
tan x / 1 = 5 / 6
tan x / 1 = 0.83
x = tan inverse o.83
x = 39.69
ANSWER: 39.69 degrees
solution 4
ReplyDeletesteps similar to 3
given
opp = 25 (5*5)
adj = 20
angle inclined = x
therefore use tan = opp / hyp
tan x / 1 = 25 / 20
tan x / 1 = 1.25
x = tan inverse 1.25
x = 51.3
ANSWER = 51.3 Degrees
whee weezy u answerin all de questions....leae some for de rest ah we na
ReplyDeletewhey!!ok
ReplyDeletethis question is part (b) of number 4.....
ReplyDeleteThe same friend from question 4 also happens to make very good paper planes, and writes a note in one and sends it to you. How far does the plane have to travel to get to you if it flies straight from him to you?
The hypotenuse is equal to the sum of the squares of the other two sides.
ReplyDeletetherfore:
the square of a a plus the square of b is equal to the square of c :
height of the building=25m
road is 20m wide
NOW...
using pythagoras theorm
A squared + B squared = C square
20 Squared + 25 Squared= C squared
400+625= C squared
now findin the root
400+625=1025
square root of 1025
= 32m
therefore the paper plane would have to travel 32 metres