Story Problems: Sketch a picture, and show all work. Round all angles to the nearest whole degree and all sides to the nearest tenth. 7. A telephone pole 15 meters high casts a shadow 10 meters long. Find the angle of elevation of the sun.

To find the angle of elevation of the sun, we can use the concept of trigonometry. Given: - Height of the telephone pole = 15 meters - Length of the shadow = 10 meters We can use the tangent function to find the angle of elevation. The tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. Let's denote the angle of elevation as θ (theta). Using the tangent function: \[ \tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}} \] In this case, the opposite side is the height of the telephone pole (15 meters) and the adjacent side is the length of the shadow (10 meters). \[ \tan(\theta) = \frac{15}{10} \] Now, we can find the angle of elevation by taking the inverse tangent (arctangent) of both sides: \[ \theta = \arctan\left(\frac{15}{10}\right) \] Let's calculate the angle of elevation using the arctangent function. Calculate the value by following steps: - step0: Calculate: \(\arctan\left(\frac{15}{10}\right)\) - step1: Reduce the fraction: \(\arctan\left(\frac{3}{2}\right)\) The angle of elevation of the sun is approximately 0.982794 radians or 56.3 degrees (rounded to the nearest whole degree).