Added in 1990 and removed in 1997, the highest advertising sign in the world was a large letter I situated at the top of the 73-story First Interstate

Question

...World Center building in Los Angeles. At a distance of 222 feet from a point directly below the sign, the angle between the ground and the top of the sign was 77.69°. Approximate the height of the top of the sign. (Round your answer to the nearest whole number.)

 

I tried to use sin(77.69)=222/x 

This led me to the answer of 227 feet, however this is incorrect. Can someone explain to me what I am doing wrong?

Answer 1

The sine function is the opposite (height of the building) / hypotenuse (distance from point to top of sign).

Here you should use the tangent function: opposite (height) / adjacent (distance from the base).

 

tan 77.69° = h / 222               determine tan

4.58257134 ≈ h / 222             multiply both sides by 222

1017.33084 ≈ h