Respuesta :
Answer:
Step-by-step explanation:
using trigonometrical ratio and considering that the journey can be represented by right angle triangle with initial point A and B are the points of the elevation of the statue which 110m apart and on the same horizontal ground with C which is the foot of the statute and D is the tip of the statue
60 minutes = 1 degree
tan 24° = h / ( 110+ x) ....(1) where x is the distance between the point B and C, the foot of the statue
tan ( 43 + (50 / 60)) = h / x .....(2)
0.96 = h/x
x = h / 0.96 = 1.04 h
replace x in the first equation
tan 24 ° = h / ( 110 +1.04h)
( 110 + 1.04 h) tan24 = h
48.98 m + 0.463 h = h
48.98 m = h - 0.463 h
48.98 m = 0.537 h
h, height of the statue = 48.98 / 0.537 = 91.21 m
Answer:
h = 91.33m
Therefore, the statue is 91.33 meters tall
Step-by-step explanation:
Let h represent the height of the statue and
d1 and d2 represent the distance between the torch and the statue at the two points.
Applying trigonometry.
For the first point;
Tan24° = h/d1
d1 = h/tan24°
For the second point;
50' = (50/60)°
60seconds = 1 degree
Tan(43+50/60)° = h/d2
d2 = h/tan(43+50/60)°
And from the question, the distance between the two points is given as 110m;
d1 - d2 = 110m
Substituting the values of d1 and d2;
h/tan24° - h/tan(43+50/60)° = 110m
h(1/tan24° - 1/tan(43+50/60)°) = 110m
h = 110m/(1/tan24° - 1/tan(43+50/60)°)
h = 110m/1.20446
h = 91.33m
Therefore, the statue is 91.33 meters tall
