Trigonometry word problems?

Question

a 12-foot ladder is leaning against a building. the ladder makes a 75 degree angle with the ground. how far is the base of the ladder from the base of the building?

and this one.

a water tower is 600 feet from an observer. a line of sight to the top of the water tank forms an angle of 28 degrees with the ground. a line of sight to the bottom oft he tank forms an angle of 26 degrees. what is the distance from the bottom of the water tank to the top of the water tank?

Answer 1

First draw a picture!

You need to know that the cosine of the 75 degree angle is the distance from the base of the ladder to the building dvided by the length of the ladder: cos(75)=d/12. So d=12*cos(75).

Draw a picture of the water tower now.

For this one you need to use the formula for tangent.

Height to the top of the tower=Ht

Then Ht/600=tan(28)

Height to the bottom of the tower=Hb

Then Hb/600=tan(26)

distance from bottom to top=Ht-Hb=600*(tan(28)-tan(26))

Answer 2

hi chelsea i am MU..ha..ha..ha ...just kidding, here...

no 1.

let the base of the ladder from the base of the building = x

use cos 75 = x/12

  x = 12 . cos 75 = 3.1 m

no 2.

you mean the height of the water tank

let it be x

and

let the distance from the point on the ground to the base of the water tower be y.

the height from the base of the tower to the base of the tank be z

then ...

tan 28 = 600 / y

y = 600 / tan 28 .

tan 26 = z / ( 600/tan 28)

z = ( 600/tan 28) . tan 26 = 550.37

then x = 600 - z = 600 - 550.37=49.63 feet.

done..phew.

see ya...

Answer 3

First question:

distance = 12cos(75)

2nd question:

total distance (top of tank to bottom of tank) = 600tan(28)-600tan(26)

Answer 4

12 = hypotenuse

so the building is the vertical side, the ground is the horizontal side (bottom) of the triangle.

You know the angle between the ground and the ladder is 75 degrees.

so cosine of 75 degrees = x/12

solve for x:

x=12cos75

x=3.1 feet

second one is similar except you know the bottom of the triangle's length - 600ft.

basically you have two triangles with different heights...so you know the angle of one triangle is 28 and the other is 26.  Use a tangent to solve for the height of both triangles and find the difference of the heights.