Geometry

Question Analysis:

This question involves Elevation and Depression Angles. The main focus is on using trigonometric relations to find the height of an object (the flagpole) given the length of a cable (hypotenuse) and the angle it makes with the ground.

 

Key Concept Explanation:

We use the sine function in a right - triangle. In a right - triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

 

Step - by - Step Solution:

Let the height of the flagpole be . The angle between the cable and the ground  and the length of the cable (hypotenuse)  meters.

We know that

Since  and the opposite side to the angle  is the height of the flagpole , and the hypotenuse  meters.

We have

Since , then

 meters

 

Common Mistakes:

Confusing the trigonometric ratios. For example, using cosine or tangent instead of sine.

Incorrectly looking up or using the value of .

 

Summary:

We were able to find the height of the flagpole by using the sine function in a right - triangle. Given the angle of the cable with the ground and the length of the cable, we applied the formula

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