3.) A box in the shape of a rectangular prism has a volume of 180 cm". The length is x cm, the
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Answer:
r = 16 units
Step-by-step explanation:
From the figure attached,
AB is the tangent drawn from a point A to the circle C.
BC = r [Radius of the circle]
Length of AC = (18 + r)
AB = 30
By the property of a tangent drawn to a circle,
"Radius of a circle and tangent are perpendicular to each other"
AB ⊥ BC
By applying Pythagoras theorem in ΔABC,
AB² + BC² = AC²
(30)² + r² = (r + 18)²
900 + r² = r² + 36r + 324
36r = 900 - 324
r =
r = 16 units
The height of the statue is 19.5 feet.
Why?
We can solve the problem using trigonometric formulas. In this case, we are going to use the trigonometric formula of the tangent.
We know that the person is standing 50ft from the statue, so, it will be the base of the two triangles formed by both angles (elevation and depression)
Using the trignometric formula, we have:
First triangle:
Second triangle:
Now, the total height of the statue will be:
Have a nice day!