Calculate the length of the shadow cast on level ground by a radio mast 90 m high when the elevation of the sun is \( 40^{\circ} \). From a window 15 m up, the angle of den \( 20^{\circ} \).

To calculate the length of the shadow cast on level ground by a radio mast 90 m high when the elevation of the sun is \( 40^{\circ} \), we can use trigonometry. Given: - Height of the radio mast = 90 m - Elevation of the sun = \( 40^{\circ} \) We can use the tangent function to find the length of the shadow cast on level ground. The tangent function is defined as: \[ \tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}} \] In this case, the opposite side is the height of the radio mast (90 m) and the adjacent side is the length of the shadow cast on level ground. Let's denote the length of the shadow cast on level ground as \( x \). Using the tangent function, we have: \[ \tan(40^{\circ}) = \frac{90}{x} \] Now, we can solve for \( x \) to find the length of the shadow cast on level ground. Calculate the value by following steps: - step0: Calculate: \(\frac{90}{\tan\left(40\right)}\) - step1: Calculate the trigonometric value: \(-80.557463\) The length of the shadow cast on level ground by a radio mast 90 m high when the elevation of the sun is \( 40^{\circ} \) is approximately 80.56 m. Next, we need to calculate the length of the shadow cast on level ground from a window 15 m up when the angle of den is \( 20^{\circ} \). Calculate the value by following steps: - step0: Calculate: \(\frac{15}{\tan\left(20\right)}\) - step1: Calculate the trigonometric value: \(6.704927\) The length of the shadow cast on level ground from a window 15 m up when the angle of den is \( 20^{\circ} \) is approximately 6.70 m. Therefore, the length of the shadow cast on level ground by a radio mast 90 m high when the elevation of the sun is \( 40^{\circ} \) is approximately 80.56 m, and the length of the shadow cast on level ground from a window 15 m up when the angle of den is \( 20^{\circ} \) is approximately 6.70 m.