Task 2: Measuring A Tall Object Far Away
Ms Doerksen is hiking in the woods behind her family's home. In order to get to the bridal path, she has to walk a bridge that crosses the Wissahickon creek as seen in the photo below. As she approaches the bridge, she measures the angle from the bridge to the center of the creek under the bridge to be $26^{\circ}$. She then walks $150 \mathrm{~m}$ to the other side of bridge that joins the bridal path and measures the angle from the bridge to the center of the creek under the bridge to be $47^{\circ}$. Using what you know thus far, how high is the bridge?

Step 1 ：Form two right triangles with the bridge's height as the opposite side and the distance from the bridge as the adjacent side.

Step 2 ：Denote the height of the bridge as h, the distance from the first point to the center of the creek under the bridge as x, and the distance from the second point to the center of the creek under the bridge as y.

Step 3 ：From the first angle, we have: \(\tan(26^\circ) = \frac{h}{x}\)

Step 4 ：From the second angle, we have: \(\tan(47^\circ) = \frac{h}{y}\)

Step 5 ：We also know that x + y = 150m (the distance between the two points).

Step 6 ：Solve these equations to find the height of the bridge.

Step 7 ：angle1 = 26, angle2 = 47, distance = 150

Step 8 ：x = 46.89, y = 103.11

Step 9 ：height = 22.87

Step 10 ：\(\boxed{\text{The height of the bridge is approximately 22.87 meters}}\)