Solve each problem. See Example 5. Height of a Building A house is 15 ft tall. Its shadow is 40 ft long at the same time that the shadow of a nearby building is 300 ft long. Find the height of the building.

Key Concepts

Similar Triangles

Similar triangles are triangles that have the same shape but may differ in size. In this problem, the house and its shadow form one triangle, while the building and its shadow form another. The ratios of the corresponding sides of similar triangles are equal, allowing us to set up a proportion to find the unknown height of the building.

Proportional Relationships

Proportional relationships occur when two quantities maintain a constant ratio. In this context, the height of the house and the length of its shadow can be compared to the height of the building and the length of its shadow. By establishing a proportion based on these relationships, we can solve for the unknown height of the building.

Trigonometric Ratios

Trigonometric ratios, such as sine, cosine, and tangent, relate the angles and sides of right triangles. Although this problem can be solved using similar triangles, understanding trigonometric ratios is essential for more complex problems involving angles. In this case, the tangent of the angle formed by the height and shadow could also be used to find the height if angles were provided.