Connor is 1.55 meters tall. At 1 p.m., he measures the length of a tree's shadow to be 39.75 meters. He stands 34.7 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

To find the height of the tree, we can use similar triangles. The ratio of Connor's height to the length of his shadow is the same as the ratio of the tree's height to the length of its shadow. Let \( h \) be the height of the tree. The ratios can be expressed as: \[ \frac{1.55}{39.75} = \frac{h}{39.75 + 34.7} \] Calculating \( 39.75 + 34.7 \) gives \( 74.45 \). Now we set up the equation: \[ \frac{1.55}{39.75} = \frac{h}{74.45} \] Cross-multiplying gives us: \[ 1.55 \times 74.45 = h \times 39.75 \] Calculating \( 1.55 \times 74.45 \) results in approximately \( 115.6135 \). Now, we divide by \( 39.75 \): \[ h = \frac{115.6135}{39.75} \approx 2.91 \] So the height of the tree is approximately \( 2.91 \) meters. Remember to always check your calculations to avoid small errors. It's easy to mix up numbers, especially when doing something as detailed as shadow measurements!