did you make a sketch??
On mine I labelled the top of the mountain as P and its perpendicular base pont as Q.
Farthest point as A and the closer point as B, AB = 2000
Look at triangle ABP
angle A=26, angle ABP = 152, then angle APB = 2
by the sine law,
BP/sin26 = 2000/sin2
BP = 2000sin26/sin2 = ....
Then in the right-angled triangle BPQ
sin28 = PQ/BP
PQ = BPsin28 = ....
A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is
26
∘
. From a point 2000 feet closer to the mountain along the plain, they find that the angle of elevation is
28
∘
.
How high (in feet) is the mountain?
2 answers
Tan26 = h/AC.
h = AC*Tan26.
Tan28 = h/(AC-2000),
h = (AC-2000)Tan28.
AC*Tan26 = (AC-2000)Tan28,
AC = (AC-2000)1.09,
0.92AC = AC-2000,
0.08AC = 2000.
AC = 25,000 ft.
Tan26 = h/25,000,
h = 12,200 Ft.
h = AC*Tan26.
Tan28 = h/(AC-2000),
h = (AC-2000)Tan28.
AC*Tan26 = (AC-2000)Tan28,
AC = (AC-2000)1.09,
0.92AC = AC-2000,
0.08AC = 2000.
AC = 25,000 ft.
Tan26 = h/25,000,
h = 12,200 Ft.
1 answer