A 5 foot tall woman stands 15 ft from a statue. She must look up at an angle of 60° to see the top of the statue. How tall is the statue?
It's easier if you drew the figure, but it's hard to draw figures here so I'll just describe it. :3
Note that the woman is 15 ft from the statue, and she looks up at an angle of 60° in order to see the top of statue. From here we can actually form a right triangle, with base 15 ft, the height unknown, and 60° angle between the hypotenuse and base.
Let h = height of triangle, which is also the height of statue minus the height of woman. Thus,
tan 60° = h / 15
h = 15 * tan 60°
h = 15*sqrt(3)
Therefore the total height of statue is h plus the height of woman, which is 15*sqrt(3) + 5 ft, or 30.98 ft
Hope this helps~ :3
To determine the height of the statue, we can use trigonometry.
Let's define some variables:
h = height of the statue
d = distance from the woman to the statue
From the problem, we know that:
The woman's height = 5 ft
The angle at which she looks up = 60°
The distance from the woman to the statue = 15 ft
To solve this, we can use the tangent function, which relates the angle of elevation to the ratio of the opposite side to the adjacent side of a right triangle.
In this case, the opposite side is the height of the statue (h), and the adjacent side is the distance from the woman to the statue (d).
Using the tangent function:
tan(60°) = h / d
We can rearrange this equation to solve for the height of the statue (h):
h = tan(60°) * d
Plugging in the given values:
h = tan(60°) * 15 ft
Using a calculator:
h ≈ 25.98 ft
Therefore, the height of the statue is approximately 25.98 feet.
To find the height of the statue, we can use trigonometry. In this case, we can use the tangent function.
Let's consider the situation. We have a right triangle formed by the woman, the statue, and the line of sight from the woman's eyes to the top of the statue. The angle between the ground and the line of sight is 60°.
The opposite side of the triangle represents the height of the statue, the adjacent side represents the distance between the woman and the statue, and the angle between them is 60°.
Using the tangent function, we can write the equation:
tan(60°) = height of the statue / distance to the statue
The tangent of 60° is √3, so we can rewrite the equation as:
√3 = height of the statue / 15 ft
To solve for the height of the statue, we'll multiply both sides of the equation by 15 ft:
√3 * 15 ft = height of the statue
The approximate value of √3 is 1.732, so:
1.732 * 15 ft = height of the statue
Calculating this, we find that the height of the statue is approximately 25.98 ft. Rounding to two decimal places, the statue is about 26 ft tall.