I only have one question # 1 find to the nearest meter the height of a church spire that casts a shadow of 50 meters when the angle of elevation of the sun measures 68 degrees.
as always, draw a diagram and you will see that
h/50 = tan68°
To find the height of the church spire, we can use trigonometry. We can set up a right triangle with the height of the spire as the vertical side and the shadow length as the horizontal side. The angle of elevation of the sun is the angle between the ground and the line from the tip of the shadow to the top of the spire.
1. Draw a diagram: Draw a vertical line to represent the church spire, and draw a horizontal line to represent the shadow on the ground. Mark the angle of elevation (68 degrees) between the ground and the line from the top of the shadow to the top of the spire.
2. Identify the right triangle: The vertical side of the triangle represents the height of the spire, the horizontal side represents the shadow length, and the line from the top of the shadow to the top of the spire represents the hypotenuse of the triangle.
3. Use trigonometry: We can use the tangent function to solve for the height of the spire. The tangent of an angle is equal to the opposite side divided by the adjacent side.
tan(angle) = opposite / adjacent
In this case, the angle is 68 degrees, the opposite side is the height of the spire, and the adjacent side is the shadow length.
tan(68 degrees) = height / 50 meters
Rearranging the equation to solve for the height:
height = tan(68 degrees) * 50 meters
4. Calculate the height: Use a scientific calculator to find the tangent of 68 degrees. Multiply the result by 50 meters to find the height. Round the final answer to the nearest meter.
height ≈ tan(68 degrees) * 50 meters
Once you have the height value, round it to the nearest meter to find the height of the church spire.