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The image shows a problem related to trigonometry involving angles of elevation and a triangle diagram. Here's a transcription of the problem:

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"A woman standing 60 m from a building looks up at a window in the building. The angle of elevation of the window is 30°. If the height of the woman’s eye level from the ground is 1.6 m, find the height of the window from the ground."

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### Solution

To solve this problem, let's define the elements given in the problem:

1. **Distance from the woman to the building:** \( d = 60 \) meters
2. **Angle of elevation to the window:** \( \theta = 30^\circ \)
3. **Height of the woman’s eye level from the ground:** \( h_1 = 1.6 \) meters

### Step 1: Height of the window above the woman's eye level
Let the height of the window above the woman's eye level be \( h_2 \).

Using the tangent function (since it relates the opposite side to the adjacent side in a right triangle):

\[
\tan(30^\circ) = \frac{h_2}{d}
\]

Substituting the values:

\[
\tan(30^\circ) = \frac{h_2}{60}
\]

We know that \( \tan(30^\circ) = \frac{1}{\sqrt{3}} \):

\[
\frac{1}{\sqrt{3}} = \frac{h_2}{60}
\]

\[
h_2 = \frac{60}{\sqrt{3}} = 20\sqrt{3} \text{ meters}
\]

### Step 2: Total height of the window from the ground
The total height of the window from the ground, \( H \), is the sum of the height of the woman's eye level and the height \( h_2 \):

\[
H = h_1 + h_2 = 1.6 + 20\sqrt{3}
\]

### Step 3: Calculation
Let's calculate the exact height:

\[
H = 1.6 + 20\sqrt{3} \approx 1.6 + 34.64 \approx 36.24 \text{ meters}
\]

### Final Answer

The height of the window from the ground is approximately **36.24 meters**.

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### Related Questions

1. What would be the height of the window if the angle of elevation were 45°?
2. How does changing the distance to the building affect the height calculation?
3. What is the relationship between the angle of elevation and the height of an object?
4. Can you solve a similar problem with a different angle and distance?
5. How would the height change if the woman stood closer to the building?
6. How can trigonometric identities help in solving such problems?
7. What is the importance of accurate angle measurement in real-life applications of trigonometry?
8. How can we derive the tangent function from the sine and cosine functions?

### Tip

When solving problems involving angles of elevation, always double-check your angle values and ensure you're using the correct trigonometric ratio.

Learn how to calculate the height of a window from the ground using the angle of elevation in this trigonometry problem. Step-by-step solution involving the tangent function and right triangle properties. Suitable for high school students studying trigonometry.

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