To calculate the height $w$ of the flagpole, we can use trigonometry. The problem involves a right triangle, where:

• The opposite side to the angle ($w$) is the height of the flagpole.
• The adjacent side (1.3 m) is the horizontal distance from the base of the pole to where the wire touches the ground.
• The angle between the wire and the ground is $68^\circ$.

The tangent of the angle relates the opposite and adjacent sides:

$\tan(68^\circ) = \frac{w}{1.3}$

Rearranging for $w$:

$w = 1.3 \cdot \tan(68^\circ)$

Calculation:

Using a calculator: $\tan(68^\circ) \approx 2.475$ $w = 1.3 \cdot 2.475 = 3.2175 \, \text{m}$

Rounding to 1 decimal place: $w = 3.2 \, \text{m}$

Final Answer:

The height of the flagpole is 3.2 m.

Would you like further explanation on this? Here are related questions for practice:

1. How does changing the angle of elevation affect the height calculation?
2. What would the height be if the horizontal distance was 2.0 m?
3. How can you calculate the length of the wire if it's not given?
4. What is the importance of rounding in practical applications?
5. How does using a different trigonometric function (e.g., sine or cosine) apply here?

Tip: Always double-check angle modes (degrees or radians) on your calculator for accurate results!