trigo
posted by trigofunctions .
Points A and B are on the same horizontal line from the foot of a hill and the angles of depression of these points from the top of the hill are 30deg and 22deg, respectively. If the distance between A and B is 75m, what is the height of the hill?

The 2 lines of sight represent the
hypotenuse of 2 rt. triangles, and
the height of the hill represents the vertical side of both triangles. The
hor. side of smaller triangle(d) is
measured from the bottom of hill to A.
The hor. side of the larger triangle
is = to d + 75m.
Tan30 = h/d, h = d * Tan30.
h = (d+ 75)* Tan22 
The 2 lines of sight represent the
hypotenuse of 2 rt. triangles, and
the height of the hill represents the vertical side of both triangles. The
hor. side of smaller triangle(d) is
measured from the bottom of hill to A.
The hor. side of the larger triangle
is = to d + 75m.
Tan30 = h/d,
h = d * Tan30.
h = (d + 75)* Tan22
Substitute d * Tan30 for h.
d * Tan30 = (d + 75) * Tan22.
Solve for d:
0.5774d = (0.4040d + 30.30.
0.5774d  0.4040d = 30.30
0.1774d = 30.30.
d = 30.30/0.1774 = 174.74m.
h = 174.74 * Tan30 = 100.9m = height
of hill. 
27
Respond to this Question
Similar Questions

math
The angle of depression of two points on opposite sides of a building are on the same horizontal level with the foot of the buiding are 58 and 49 respectively from the top of the building. If the building is 38m tall, calculate the … 
trig
From the top of a hill 700 ft. high, an observer notes that the angles of depression of two successive markerstones on a level ground, which leads straight away from the hill are 5 degree and 15 degree respectively. Find the distance … 
trigonometry
From the top of a hill 700 ft high an observer notes that the angles of depression of two successive markerstones on a level ground, which leads straight away from the hill are 5 degree and 15 degree respectively. Find the distance … 
trigonometric problem
Point A and B are on the same horizontal line with the foot of a hill and the angles of depression of these points from the top of hill are 32° and 22° respectively. If the distance between A and B is 80 meters, what is the height … 
trigonometry
a tower 150 meter is situated at the top of the hill.At a point 650 m down the hill.The angle between the surface of the hill and the line of sight to the of the tower is 12degrees 30 '.Find the inclination of the hill to a horizontal … 
math
Street  Horizontal  Vertical rise Distance ft. of street ft. ___________________________________ Dixie hill 80.  40 Bell hill  80.  20 Liberty hill 80.  60 Which hill is the steepest? 
Math help please
Which hill described in the table is the steepest? 
applilcations of trigonometry
A surveyor wants to find the height of the top of a hill. He observes that the angles of elevation of the top of the hill at points C and D, 300m apart, lying on the base of the hill and on the same side of the hill are 30° and 45° … 
Math "Need Help Asap"!
9.)Which hill described in the table is the steepest? 
Maths
the angles of of evolution of the top of a hill from the City centres of two towns on either side of the hill are observed to be 30Â° and 60Â° respectively. if the distance of hill of the top from the city centre of first is 9 …