Chalkboard Explanation Video
Step-by-step Derivation
1 Identify the given information and unknown
Distance from base =15 m
Angle of elevation =60∘
Height of tower =h=? 2 Choose the appropriate trigonometric ratio tanθ=AdjacentOpposite tan60∘=15h$$
(Trigonometry, Angle of elevation, Tangent, Right triangle, Height)
Get the complete, step-by-step math solution for: "Chalkboard Explanation Video Step-by-step Derivation 1 Identify the given information and unknown Distance from base = 15 m Angle of elevation = 60^ H...". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Identify Given Information
First, we identify the given information from the problem statement. We are given the distance from the base of the tower to the observation point, which is 15 m. We are also given the angle of elevation to the top of the tower, which is 60∘. Our goal is to find the height of the tower, which we denote as h.
Step 2: Choose Trigonometric Ratio
To relate the height of the tower (opposite side) and the distance from the base (adjacent side) to the angle of elevation, we use the tangent trigonometric ratio. The tangent of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
Step 3: Substitute Values and Solve for Height
Now, we substitute the given values into the tangent equation. The angle θ is 60∘, the opposite side is h, and the adjacent side is 15 m. We know that tan60∘=3. By rearranging the equation, we can solve for h.