Questions: A 6.2 ft tall man creates a 67° angle of elevation when he looks up to the top of a building from the ground. If he stands 20 feet from the building, how tall is the building?

Solution Steps

To find the height of the building above the man's eyes, we first calculate the tangent of the angle of elevation \( \theta = 67^{\circ} \): \[ \tan(67^{\circ}) \approx 2.35585236582375 \]

Using the tangent value, we can find the height above the man's eyes. The formula is given by: \[ \text{Height above eyes} = \tan(67^{\circ}) \times \text{distance from building} \] Substituting the known values: \[ \text{Height above eyes} = 2.35585236582375 \times 20 \approx 47.1170473164751 \text{ feet} \]

Finally, we add the height of the man to the height above his eyes to find the total height of the building: \[ \text{Total height of the building} = \text{Height of the man} + \text{Height above eyes} \] Substituting the values: \[ \text{Total height of the building} = 6.2 + 47.1170473164751 \approx 53.3170473164751 \text{ feet} \]

Final Answer