Question

The tip of the empire state building is 1,454 ft off the ground. How far away from it would you have to stand to make a 25° angle with the top? Round your answer to 2 decimal places

Answer 1

Answer:

1604.31 feet

Step-by-step explanation:

Picture yourself facing directly at the building. This is our opposite side in relation to the angle. The distance between you and the top of the building will be the hypotenuse. Therefore, we use the sine function:

$sin\theta=\frac{opposite}{hypotenuse}\\ \\sin(90^\circ-25^\circ)=\frac{1454}{x}\\\\xsin65^\circ=1454\\\\x=\frac{1454}{sin65^\circ}\\\\x\approx1604.31$

Therefore, you would need to stand about 1604.31 feet away from the building to form a 25° angle with the top of the building.

Answer 2

$\\ \rm\rightarrowtail tan\theta=\dfrac{Perpendicular}{Base}$

$\\ \rm\rightarrowtail tan25=\dfrac{1454}{x}$

$\\ \rm\rightarrowtail x=1454/0.4663076581549$

0.4663076581549x=3118.1130624208ft[/tex]

• x=3118.11ft