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Welcome to our exploration of basic trigonometric ratios!Let's start with a right triangle, which is the foundation of trigonometry.In this triangle, we have an angle theta, and three important sides.The side opposite to our angle theta is called the opposite side.The side next to our angle is called the adjacent side.And the longest side, opposite to the right angle, is called the hypotenuse.The sine of an angle is the ratio of the opposite side to the hypotenuse.The cosine is the ratio of the adjacent side to the hypotenuse.And the tangent is the ratio of the opposite side to the adjacent side.Let's calculate these ratios for our triangle. If the opposite side is 3 units and the adjacent side is 4 units, the hypotenuse would be 5 units.The unit circle is a powerful tool for understanding trigonometric ratios.As we move a point around the circle, we can measure angles in both degrees and radians.The unit circle is divided into four quadrants, each affecting the signs of trigonometric ratios.As we complete a full rotation around the circle, notice how the trigonometric ratios change in each quadrant.In our first example, we'll calculate a building's height using the tangent ratio.Standing 20 meters from a building and looking up at a 40-degree angle, we can use tangent to find its height.Our second example involves measuring the width of a river using trigonometry.Using a 30-degree angle and the river's width of 30 meters, we can calculate the distance to the opposite bank.Our final example demonstrates how to find a mountain's height using measurements from two different positions.By taking angle measurements of 60 and 45 degrees from two points 100 meters apart, we can determine the mountain's height using a system of equations.Let's review the key applications of trigonometry in real-world situations.Thank you for learning about practical applications of trigonometry!