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Howard is standing 109 yards from the bottom of a water reservoir. He estimates that the angle of elevation to the top of the water reservoir is about 50°. About how far is Howard from the top of the water reservoir?

Respuesta :

Answer:

70.1 yards

Step-by-step explanation:

See the attached diagram.

Let AC is the reservoir with A as the bottom and C is the top.

Now, B is the position of Howard which is 109 yards from A i.e. AB = 109 yards.

Again, the angle elevation from B to C is 50 degrees.

So, ∠ ABC = 50°  

Now, [tex]\cos 50 = \frac{AB}{BC} = \frac{109}{x}[/tex]

⇒ x = 109 cos 50 = 70.1 yards.

Therefore, the distance between the top of the reservoir and Howard i.e. BC is equal to 70.1 yards. (Answer)

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