To solve the problem of finding the height of the tree that the hunter is viewing, we can use some basic trigonometry. Let's break down the problem step-by-step. ### Step 1: Understand the Situation - The hunter is 1.6 meters tall. - He is viewing a bird at the top of a tree at an angle of 45°. - The horizontal distance from the hunter to the base of the tree is 10.4 meters. ### Step 2: Visualize the Problem Imagine a right triangle formed by: - The height of the tree (which we need to find). - The horizontal distance from the hunter to the tree (10.4 m). - The line of sight from the hunter's eyes to the bird at the top of the tree. ### Step 3: Set Up the Triangle 1. The height of the tree can be represented as \( h \). 2. The height of the hunter's eyes from the ground is 1.6 m. 3. Therefore, the height of the tree above the hunter's eyes is \( h - 1.6 \) m. ### Step 4: Use Trigonometry Since the angle of elevation to the bird is 45°, we can use the tangent function, which relates the angle of a right triangle to the opposite side and the adjacent side. The formula for tangent is: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] In our case: - \( \theta = 45° \) - The opposite side is \( h - 1.6 \) (the height of the tree above the hunter's eyes). - The adjacent side is 10.4 m (the distance from the hunter to the tree). ### Step 5: Calculate Using the Tangent Function For \( \theta = 45° \): \[ \tan(45°) = 1 \] This means: \[ 1 = \frac{h - 1.6}{10.4} \] ### Step 6: Solve for \( h \) Now, we can set up the equation: \[ h - 1.6 = 10.4 \] Adding 1.6 to both sides gives: \[ h = 10.4 + 1.6 \] \[ h = 12.0 \text{ m} \] ### Conclusion The height of the tree is **12.0 m**. Therefore, the correct option is **B**. ### Explanation of Other Options - **Option A (9.0 m)**: This option is incorrect because it underestimates the height of the tree. It does not account for the height of the hunter. - **Option C (8.8 m)**: This option is also incorrect as it similarly underestimates the height of the tree and does not consider the correct angle of elevation. - **Option D (10.4 m)**: This option is incorrect because it only considers the horizontal distance and does not account for the height of the hunter or the angle of elevation. ### Revision Summary - Use trigonometry (specifically tangent) to relate angles and sides in right triangles. - Remember to account for the height of the observer (hunter) when calculating the total height of an object (tree). - The angle of elevation is crucial in determining the height above the observer's eye level. - Always check your calculations to ensure that all components of the problem are considered.