Example 1 Evelyn Granville, who is 1.5 m tall, is standing 20 m from the base of a building. She sights the top of the building with an angle of elevation of \( 58^{\circ} \). Find the height of the building.

To find the height of the building, we can use some trigonometry! Since Evelyn is 1.5 m tall, to find the total height of the building, we can use the tangent function in relation to the angle of elevation. First, we'll find the height from Evelyn’s eyes to the top of the building using the formula: \[\text{Height} = \tan(\theta) \times \text{Distance}\] where \(\theta = 58^{\circ}\) and the distance is 20 m. Calculating this gives us: \[\text{Height} = \tan(58^{\circ}) \times 20 \approx 30.53 \text{ m}\] Now, since we need to add Evelyn's height to find the total height of the building: \[\text{Total Height} = 30.53 \text{ m} + 1.5 \text{ m} \approx 32.03 \text{ m}\] So, the height of the building is approximately 32.03 m. --- Now for a little extra fun: Evelyn might not be the only one standing outside, looking up! Did you know that the principles of right triangles are used everywhere? From determining how tall skyscrapers are to helping architects create buildings that fit harmoniously into the skyline, trigonometry provides the backbone of construction. And here’s a common mistake: remember to ensure your calculator is in the correct mode—degrees or radians—before doing the calculations! Many a student has miscalculated because they were in the wrong mode. Double-check to avoid those sneaky errors!