A Hawaiian resort has ancient wood-carved statues. One of the statues measures 15 feet tall. If a model is sketched using the scale \( 0.75 \mathrm{~cm}=1.5 \) feet, how tall is the model of the statue?

To find the height of the model of the statue, we first need to convert the height of the actual statue from feet to centimeters using the given scale. The scale states that \( 0.75 \) cm corresponds to \( 1.5 \) feet. We can find out how many centimeters correspond to \( 15 \) feet by setting up a proportion. First, we find the number of centimeters per foot: \[ \text{cm per foot} = \frac{0.75 \text{ cm}}{1.5 \text{ feet}} = 0.5 \text{ cm/foot} \] Now, we can convert the height of the statue (15 feet) to centimeters: \[ \text{Height in cm} = 15 \text{ feet} \times 0.5 \text{ cm/foot} = 7.5 \text{ cm} \] Now, we need to find the height of the model using the same scale. Since \( 0.75 \) cm represents \( 1.5 \) feet, we can find the height of the model by using the same ratio. To find the height of the model, we can set up the following proportion: \[ \frac{\text{Height of model}}{7.5 \text{ cm}} = \frac{0.75 \text{ cm}}{1.5 \text{ feet}} \] To find the height of the model, we can calculate: \[ \text{Height of model} = \frac{0.75 \text{ cm}}{1.5 \text{ feet}} \times 15 \text{ feet} \] Calculating this gives: \[ \text{Height of model} = 0.75 \times 10 = 7.5 \text{ cm} \] Thus, the height of the model of the statue is: \[ \boxed{7.5 \text{ cm}} \]