Final answer:
To calculate the height of the flagpole, we use trigonometric functions to solve for the opposite side of a right triangle formed by the flagpole, its shadow, and the angle at which the shadow falls, which is determined by the difference between the slope angle and the sun's angle of elevation.
Step-by-step explanation:
To find the length of the flagpole on a slope, we can use trigonometry. The flagpole, shadow on the slope, and the line from the top of the flagpole to the end of the shadow form a right triangle. Given that the slope makes an angle of 15 degrees with the horizontal and the angle of elevation of the sun is 20 degrees, the angle at which the shadow falls from the flagpole will be the difference between these two angles, which is 5 degrees (since the flagpole is perpendicular to the horizontal).
The flagpole's height (h) is the opposite side to the 5 degrees angle, and the shadow's length (150 m) is the adjacent side. We can use the tangent function here, which is defined as the opposite side divided by the adjacent side. Therefore:
tan(5 degrees) = h / 150 m
By solving for h, we get:
h = 150 m * tan(5 degrees)
After calculating the tangent of 5 degrees and multiplying by 150 m, we will find the approximate height of the flagpole to the nearest tenth of a meter.