Question

From a point on the ground 12 ft. from the base of a flagpole, the angle of elevation of the top of the pole measures 53°. How tall is the flagpole?

Answer 1

Given :

• Base of the triangle (The figure is forming a triangle) = 12 ft
• Angle to be considered as theta = 53°

To Find :

• The hieght of the flagpole ??

Concept:

Now, as we can see in the figure, the base lenght is given, and the angle is given, so we need to find our the value of hieght.

Using the trigonometric ratio of sides, we get that we should use the tan function for Finding hieght.

• Tan A = OS/AS

here, OS = opposite side

AS = Adjacent side

Solution :

Given, Theta = 53°

Side Adjacent to Theta = 12 ft

Side opposite to Theta = ??

So, using the tan function:

$\displaystyle \rm \implies tan \theta = \frac{side \: opposite}{side \: adjacent}$

$\displaystyle \rm \implies tan 53 {}^{ \circ} = \frac{side \: opposite}{12}$

$\displaystyle \rm \implies \frac{4}{3} = \frac{height}{12}$

$\displaystyle \rm \implies \frac{4 \times 12}{3} = {height}$

$\displaystyle \rm \implies hieght = \frac{4 \times \cancel{12}}{ \cancel{3}}$

$\displaystyle \rm \implies hieght = 4 \times 4$

$\red{ \underline{ \boxed{\displaystyle \rm \implies height = 16ft}}}$

So, the hieght of flag pole = 16 ft

Final Answer:

We got that :

• Hieght of flag pole = 16 feet