Answer:60ft
Step-by-step explanation:The height of the flagpole is approximately
60
feet.
Explanation:
Always try to draw a diagram.
enter image source here
We know that there is a right angle between the ground and the building. Therefore, we can use the 3 basic trig ratios instead of the sine or cosine law to solve this problem.
Since the angle in the corner of the larger right triangle measures
42
˚
, the top angle in this triangle measures
180
˚
−
90
˚
−
42
˚
=
48
˚
.
By basic trig ratios, we can find the height of the building with the flag pole on top, call it
H
.
tan
42
˚
1
=
H
500
H
=
500
tan
42
˚
I would keep it in exact form until the last step.
We now devise an expression for the height of the building (without the flag pole). Call it
a
tan
38
˚
1
=
a
500
a
=
500
tan
38
˚
We can now state that
h
=
H
−
a
h
=
500
tan
42
˚
−
500
tan
38
˚
h
≈
59.559
≈
60
feet
Hopefully this helps!
Answer link
EET-AP
Apr 10, 2017
The flagpole is
60
f
t
in height to the nearest foot.
Explanation:
1) The flagpole is on top of a building.
2)Angles of elevation both measured from point
500
f
t
from building
3) Angle of elevation to the top of building is
38
d
e
g
4) Angle of elevation to the top of flagpole is
42
d
e
g
The information above will provide us with two right angle triangles, one smaller one inside a larger one.
Both will have a base of
500
f
t
.
The smaller triangle will have a base angle
β
of
38
deg opposite the
90
deg, and the larger triangle will have a base angle
β
of
42
deg.
From this information we can find the heights of the building and the building + pole using the definition of the tangent of the two base angles
β
:
tan
(
β
)
=
o
p
p
a
d
j
where the
o
p
p
is the height and the
a
d
j
is the
500
f
t
o
p
p
(
b
u
i
l
d
)
=
tan
(
38
)
⋅
(
500
f
t
)
=
390.6
f
t
=
height of building
o
p
p
(
f
l
a
g
)
=
tan
(
42
)
⋅
(
500
f
t
)
=
450.2
f
t
=
height of building + pole
Then to the nearest foot the height of the flagpole is:
450.2
f
t
−
390.6
f
t
=
60
f
t
![A_{2}=2* \frac{b*h}{2} \\ \\ A_{2}= [r*sen(40)][r*cos(40)]\\ \\A_{2}= r^{2}*sen(40)*cos(40)](https://tex.z-dn.net/?f=A_%7B2%7D%3D2%2A%20%5Cfrac%7Bb%2Ah%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%20A_%7B2%7D%3D%20%5Br%2Asen%2840%29%5D%5Br%2Acos%2840%29%5D%5C%5C%20%20%5C%5CA_%7B2%7D%3D%20r%5E%7B2%7D%2Asen%2840%29%2Acos%2840%29)
