Shadow Length

[nycmathguy]

Section 5.2

I am only doing 62 (a).

Part (a)

sin(90° - theta) = cos(theta).

s = h[cos(theta)/sin(theta)]

cos(theta)/sin(theta) = cot(theta)

So, s = h cot(theta).

We move on to Section 5.3 aka Trigonometric Equations.

 

[nycmathguy]

Can you please do parts (b) - (d)? I need more study notes. Thanks. We move on to Trigonometric Equations which is Section 5.3.

 

[MathLover1]

b.

To start we will use values of θ between 0° and 90° .

if h=5
s = 5cot(theta)

theta........................s = 5cot(theta)

0°...........................s = 5cot(0°)=
30°...........................s = 5cot(30°)=8.66
45°...........................s = 5cot(45°)=5
60°...........................s = 5cot(60°)=2.89
90°...........................s = 5cot(90°)=0

c.

minimum length is at 90°

d.
at the midpoint of the day: noon

 

[nycmathguy]

b.

To start we will use values of θ between 0° and 90° .

if h=5
s = 5cot(theta)

theta........................s = 5cot(theta)

0°...........................s = 5cot(0°)=
30°...........................s = 5cot(30°)=8.66
45°...........................s = 5cot(45°)=5
60°...........................s = 5cot(60°)=2.89
90°...........................s = 5cot(90°)=0

c.

minimum length is at 90°

d.
at the midpoint of the day: noon

Great work. Thank you.I assume (a) is right.

 

[MathLover1]

(a) is right

 

[nycmathguy]

(a) is right

Give me a few days to work on the remaining problems. I think the weekend is better for me. I posted 10 "crazy" math problems in the Algebra forum for your entertainment. Enjoy.