Question

will someone help me solve this please? (On a morning of a day when the sun will pass directly overhead the shadow of a 72-ft building on level ground is 96 ft long. At the moment in question, the angle theta the sun makes with the ground is increasing at the rate of .26 radians/minute. At what rate is the shadow decreasing (in inches)"

Answer 1

Can u tell me \[\tan(\theta)..??\]

Answer 2

\[\tan(\theta)=\frac{ 72 }{ x }\]
\[\frac{ d }{ dt }\tan(\theta)=\frac{ d }{ dt }(\frac{ 72 }{ x })\]
\[\sec^{2}(\theta)\frac{ d{\theta} }{ dt }=-\frac{ 72 }{ x^{2} }\frac{ dx }{ dt }\]
Now can you find the required?

Answer 3

Any how you will get\[\frac{ dx }{ dt }=-52\frac{ ft }{ \min }\]

Answer 4

sorry, my internet went out, but the website i did my homework on says that that answer is wrong, the final answer is actually 10.9?