SOLUTION: Can you please help me with this problem. I have tried and tried and I am not sure. I need help asap. Thank you. A BUILDING CASTS A SHADOW 23FT LONG WHEN THE ANGLE OF ELEVATI

Algebra ->  Triangles -> SOLUTION: Can you please help me with this problem. I have tried and tried and I am not sure. I need help asap. Thank you. A BUILDING CASTS A SHADOW 23FT LONG WHEN THE ANGLE OF ELEVATI      Log On


   

Question 144862: Can you please help me with this problem. I have tried and tried and I am not sure. I need help asap. Thank you.
A BUILDING CASTS A SHADOW 23FT LONG WHEN THE ANGLE OF ELEVATION OF THE SUN IS 52 DEGREES, FIND THE HEIGHT OF THE BUILDING CORRECT TO THE NEAREST INTEGER.
***I MUST SHOW ALL WORK SO PLEASE DO SO FOR ME*** THANK YOU VERY MUCH***
THE PICTURE SHOWS RIGHT TRIANGLE WITH ONE 90 DEGREE ANGLE AND ONE 52 DEGREE ANGLE. I KNOW THE OTHER ANGLE WOULD BE 38 DEGREES. THE ONLY LENGTH I ASSUME GIVEN WOULD BE 23FT WHICH IS ONE LEG THE OTHER LEG IS NOT GIVEN NOR HYPOTENUSE.
THANK YOU SO MUCH IN ADVANCE! =]
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Ok, you can use the tangent function to solve this problem.
Remember that in a right triangle, such as you have here, the tangent of 52 degrees (tan(52) is the ratio of the side opposite the 52-degree angle (that's the height of the building, h) divided by the side adjacent to the 52-degree angle (that's the length of the building's shadow, or 23 ft.)
So, we can write:
Tan%2852%29+=+h%2F23 Now you multiply both sides by 23 to get:
23%2Atan%2852%29+=+h You can do this in your calculator.
h+=+29.4386 Round the the nearest integer:
h+=+29 feet.