Trig
posted by Alexis .
A billboard rests on top of a base. From a point level with the bottom of the base, the angle of elevation of the bottom of the billboard is 26 degrees and the top of the billboard is 31 degrees. From a point 21 meters further away, the angle of elevation to the top of the billboard is 17 degrees. Find the height of the billboard.

Trig 
Reiny
Let's make a diagram.
Call the top of the billboard A and the bottom of the billboard E, and the point below AE we will call C, where C is at ground level.
Label D as the first point of observation, and B as the second point of observation, so that BD = 21
Let's look at triangle ABD.
Angle BDA = 18031 = 149º
then angle BAD = 14º
and angle B = 17º
So by the sine law,
AD/sin17 = 21/sin14
We can find AD.
Now let's look at triangle ADC which is rightangled.
cos 31 = DC/AD, thus we can find DC
also sin 31 = AC/AD, giving us AC
and finally in triangle DEC
tan 26 = EC/DC giving us EC
so the billboard's height is AC  EC
Do not round off preliminary answers, good luck. 
Trig 
drwls
Let a be the original horizontal distance from which the billboard is viewed.
Let h be the height of the billboard.
Let b be the height of the base.
b/a = tan 26 = 0.4877
(b+h)/a = tan 31 = 0.6009
(b+h)/(a + 21) = tan 17 = 0.3057
You have to solve three equations in three unknowns (a, b, h) to get h.
Respond to this Question
Similar Questions

Trigonometry
If someone could tell me if this is correct, it would really help me out. Problem: A statue 20 feet high stands on top of a base. From a point in front of the statue, the angle of elevation to the top of the statue is 48 degrees, and … 
trig
A BILLBOARD PAINTER HAS BEEN ASSIGNED THE TASK OF CHANGING THE ADVERTISMENT ON A 20FT BILLBOARD,THE BOTTOM OF WHICH IS 15FT OFF THE GROUND.AFTER EXAMINING THE SITE, SHE IDENTIFIES TWO AREAS ON THE GROUNG UNDER THE SIGN THAT ARE STURDY … 
calculus
a billboard 20ft tall is located on top of a building with its lower edge 60 ft above the level of a viewers eye. how far from a point directly below the sign should a viewer stand to maximize the angle (theta) between the lines of … 
Mathtrig
A stairway runs up the edge of the pyramid. From bottom to top the stairway is 92 m long. The stairway makes an angle of 70° to the base edge, as shown. A line from the middle of one of the base edges to the top of the pyramid makes … 
math
The top of a billboard is 30 feet above ground. The billboard casts a 235 feet long shadow. What is the angle of elevation from the tip of the shadow to the sun? 
math
A point is directly below a window. Another point B is 15 m from A and at the same horizontal level. From B angle elevation of the top of the bottom of the window is 300 and the angle elevation of the top of the widow is 350. Calculate … 
Math
A billboard is 2.5 times as long as it is wide. The area of the actual billboard is 2,250 square feet. A scale drawing is made of the billboard and the area of the scale is 160 square inches. What is the scale used in the scale drawing? 
math
A community park wants to place a rectangular billboard to inform guests of their new attractions. Suppose the length of the billboard to be placed is 5m longer than its width and the area is 500m2. What will be the length and the … 
Mathematical measurement
Find the ratio of the longest side to the perimeter of the righttriangularshaped billboard. A scalene triangular billboard that says "Ski Whitetop" is designed to look like a snowpeaked mountain with a road leading up to the … 
Math
a scale drawing of a billboard uses the scale 4cm: 9ft. The length of the billboard in the drawing is 11cm. How long is the actual billboard.