A person standing on the ground observes the top of a tree at an angle of elevation of 45 degrees. If the person is 10 meters away from the base of the tree, what is the height of the tree?

To determine the height of the tree, we can use trigonometry, specifically the tangent of the angle of elevation. ### Given: - **Angle of elevation (θ):** 45 degrees - **Distance from the person to the base of the tree (adjacent side):** 10 meters ### Objective: Find the **height of the tree (opposite side)**. ### Using the Tangent Function: The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] Plugging in the known values: \[ \tan(45^\circ) = \frac{h}{10} \] We know that: \[ \tan(45^\circ) = 1 \] So, \[ 1 = \frac{h}{10} \] ### Solving for \( h \): \[ h = 10 \times 1 = 10 \text{ meters} \] ### **Answer:** The tree is 10 meters tall.