Contact: Ms. Osborne (592) 6796884 or Mr. Walker (592) 6869189 A. mathat: [email protected] and bottom of a flag-staff standing on the tower as \( 62^{\circ} \) and \( 60^{\circ} \) respectively. Calculate the height of the flagstaff.

To calculate the height of the flagstaff, we can use trigonometry. Let's denote the height of the flagstaff as \( h \), the distance from the base of the tower to the point where the angles are measured as \( d \), and the height of the tower as \( H \). 1. **Understanding the Angles**: - The angle of elevation from the point on the ground to the top of the flagstaff is \( 62^\circ \). - The angle of elevation from the same point to the top of the tower (without the flagstaff) is \( 60^\circ \). 2. **Setting Up the Equations**: - From the point on the ground to the top of the flagstaff: \[ \tan(62^\circ) = \frac{h + H}{d} \] - From the point on the ground to the top of the tower: \[ \tan(60^\circ) = \frac{H}{d} \] 3. **Expressing \( H \) in terms of \( d \)**: - Rearranging the second equation gives: \[ H = d \cdot \tan(60^\circ) \] 4. **Substituting \( H \) into the first equation**: - Substitute \( H \) into the first equation: \[ \tan(62^\circ) = \frac{h + d \cdot \tan(60^\circ)}{d} \] - Rearranging gives: \[ d \cdot \tan(62^\circ) = h + d \cdot \tan(60^\circ) \] - Thus: \[ h = d \cdot \tan(62^\circ) - d \cdot \tan(60^\circ) \] - Factoring out \( d \): \[ h = d \cdot (\tan(62^\circ) - \tan(60^\circ)) \] 5. **Calculating the Tangents**: - Using a calculator: \[ \tan(62^\circ) \approx 1.8807 \] \[ \tan(60^\circ) \approx 1.7321 \] - Therefore: \[ \tan(62^\circ) - \tan(60^\circ) \approx 1.8807 - 1.7321 = 0.1486 \] 6. **Final Expression for Height**: - The height of the flagstaff can be expressed as: \[ h = d \cdot 0.1486 \] - To find the exact height, we need the distance \( d \). If \( d \) is known, you can substitute it into the equation to find \( h \). If you have a specific value for \( d \), please provide it, and I can calculate the height of the flagstaff for you.