A flagpole casts a shadow of 6.3 m when the angle of elevation to the sun is 65 degrees. What is the height of the flagpole?

The shadow length is the adjacent side to the angle of elevation, and the height of the flagpole is the opposite side.
Given:

• Shadow length (adjacent) = $6.3 \text{ m}$
• Angle of elevation ($\theta$) = $65^\circ$
• Height of flagpole (opposite) = $h$ (unknown)

Since we have the adjacent side and need to find the opposite side, we use the tangent function:

$$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$

$$h = 6.3 \times \tan(65^\circ)$$ $$h = 6.3 \times 2.1445069$$ $$h \approx 13.51 \text{ m}$$

The height of the flagpole is approximately $13.51 \text{ m}$.