The distance from point P to the foot of the flagpole is 13.42m. So, The height of the flagpole will be 17.7 m.
What are the six trigonometric ratios?
Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.
In a right-angled triangle, two such angles are there which are not right-angled(not of 90 degrees).
The slanted side is called the hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called the base.
We know that
[tex]tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}[/tex]
Let x be the distance from point P to the foot of the flagpole.
So, From point P the height h of the flagpole will be
[tex]tan(53) = \dfrac{height}{x}\\\\tan(53) x = h\\\\h = 1.32x[/tex]
From point Q, the height h will be
[tex]tan(28) = \dfrac{height}{20+x}\\\\tan(28) (20+x )= h\\\\h = 0.53 (20+x )[/tex]
From both values of h, we get
x = 13.42
Put the value of x in the first value of h,
h = 1.32 ( 13.42)
h = 17.7
Hence, the height of the flagpole will be 17.7 m.
Learn more about trigonometric ratios here:
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