While sailing toward a statue, a sailor in a boat observed that at a certain point, the angle of elevation of the tip of the torch was 24 degrees. After sailing another 110 meters toward the statue, the angle of elevation became 43 degrees 50 prime. How tall is the statue?

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

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

the answer is b.)

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