A flagpole casts a shadow s feet long when the angle of elevation of the sun is a. Write an expression to find the height of the flagpole.
The possible answers are:
a. s/tan a
b. s cos a
c. s sin a
d. s/sin a
e. s tan a
If the height is h, the shadow length is given by
h = s tan a
Tp rove this to yourself, draw a triangle with sides that are: (a) the verical flagpole, (b) the level ground and (c) a ray of sunlight passing from the top of the pole to the end of the shadow.
Thanks
The correct expression to find the height of the flagpole when the angle of elevation of the sun is a and the shadow cast is s feet long is:
a. s/tan a
So, the answer is a. s/tan a.
To find the height of the flagpole, we can use the concept of trigonometry and right triangles.
Let's consider a right triangle formed by the flagpole, its shadow, and a line from the top of the flagpole to the tip of its shadow. The angle between the ground and the line from the top of the flagpole to the tip of its shadow is the angle of elevation (a) of the sun.
Now, in a right triangle, the side opposite to an angle is known as the height (h) of the triangle. In this case, the height of the flagpole is what we are trying to find.
The side adjacent to the angle (a) is the length of the shadow (s).
If we recall the trigonometric functions, the tangent (tan a) of an angle is defined as the ratio of the length of the side opposite to the angle to the length of the side adjacent to the angle.
So, based on the given information, the expression to find the height (h) of the flagpole can be written as:
h = s * tan a
Therefore, the correct expression to find the height of the flagpole is (e) s tan a.