MATH SOLVE

2 months ago

Q:
# HELP PLEASE!! As John walks 16 ft towards a chimney, the angle of elevation from his eye to the top of the chimney changes from 30° to 45°. Identify the height of the chimney from John's eye level to the top of the chimney rounded to the nearest foot.

Accepted Solution

A:

Answer: 22 feet.Step-by-step explanation: Note that there are two right triangles in the figure attached: ACD and BCD. Where "h" is the height of the chimeney from John's eye level to the top of the chimney. You need to use the trigonometric identity [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] for this exercise. For the triangle BCD: [tex]tan(45\°)=\frac{h}{x}[/tex] Solve for h: [tex]h=xtan(45\°)\\h=x[/tex] For the triangle ACD: [tex]tan(30\°)=\frac{h}{x+16}[/tex] Substitute [tex]h=x[/tex] and solve for h: [tex]tan(30\°)=\frac{h}{h+16}\\\\(h+16)(tan(30\°))=h\\\\0.577h+9.237=h\\\\9.237=h-0.577h\\\\9.237=0.423h\\\\h=\frac{9.237}{0.423}\\\\h=21.836ft[/tex] Rounded to the nearest foot: [tex]h=22ft[/tex]