Mathematics: If a dart were thrown randomly at the dart board shown below, what is the probability that it would land in the bull s-eye (with radius 2 mm)? A) 8% B) 2% C) 1% D) 3%

If a dart were thrown randomly at the dart board

natalie2sheffield

06.01.2020

The height of the tower is 141.74 meters.

Step-by-step explanation:

See the attached diagram.

Let the position of the tower os AB with A as the base and B is the top.

Now, angle of elevation of point B from point C is 50°, and the from point D is 40°, and hence, CD = 50 meters,

Now, from Δ ABC, $\tan 50 = \frac{AB}{AC} = \frac{x}{AC}$

⇒ $AC = \frac{x}{\tan 50} = 0.839x$ .......... (1)

Again, from Δ ABD, $\tan 40 = \frac{AB}{AD} = \frac{x}{AD}$

⇒ $AD = \frac{x}{\tan 40} =1.192x$ .......... (2)

Now, DC = AD - AC

⇒ 50 = 1.192x - 0.839x

⇒ 50 = 0.353x

⇒ x = 141.74 meters.

Hence, the height of the tower is 141.74 meters. (Answer)

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