When the sun is 30° above the horizon, shadow of one tree is 17-3 m long. What is the height of this tree ?

To find the height of the tree, we use the trigonometric tangent function, which relates the angle of elevation to the ratio of the opposite side (height) and the adjacent side (shadow length). The problem states the sun is 30° above the horizon, making the angle of elevation 30°. The shadow length is given as 17.3 m (noted as 17-3 m in the prompt, which corresponds to 10√3 or approximately 17.32 m). Using the formula tan(θ) = height / shadow, we have tan(30°) = height / 17.32. Since tan(30°) is 1/√3 (approximately 0.577), the calculation becomes height = 17.32 × (1/√3). This simplifies to height = 17.32 / 1.732, resulting in exactly 10 meters. Thus, a tree with a height of 10 m casts a shadow of approximately 17.32 m when the sun is at a 30° altitude.