Question

A flagpole at a right angle to the horizontal is located on a slope that makes an angle of 18° with the horizontal. The flagpole casts a 12-meter shadow up the slope when the angle of elevation from the tip of the shadow to the sun is 19°. What is the height of the pole?

Answer 1

To find the height of the flagpole, use the tangent function with the given angle of elevation and the length of the shadow.

Step-by-step explanation:

To find the height of the flagpole, we can use trigonometry. Let's label the height of the flagpole as 'h'. The 12-meter shadow is the adjacent side of the right triangle formed by the flagpole and the ground, and the angle of elevation is the opposite side. We can use the tangent function to find the height of the pole:

tan(19°) = h/12

h = 12 * tan(19°)

Using a calculator, we find that h ≈ 4.33 meters. Therefore, the height of the flagpole is approximately 4.33 meters.

Answer 2

height = 9.28m

Step-by-step explanation:

Sum of angle in a triangle = 180°

To find the third angle, we have

180° = 71° + 62° + α

180° = 133° + α

α = 180° - 133°

α = 47°

To find the height use sine rule

h/sin47° = 12/sin 71°

h(sin71°) = 12sin47°

h = 12sin47° / sin71°

h = 12(0.7314) / 0.9455

h = 8.7768/0.9455

h = 9.28m