From a point 100 m from a building the angles of elevation of the top and bottom of a flagpole atop a building are 54.5 degrees and 51.8 degrees, respectively. How tall is the flagpole?

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

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

if i put something wrong your not gonna like it so rather not say nothing.