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# what is the distance from the tip of the shadow to the top of his head?

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4 Adam, who is 5'6" tall, notices his shadow on the sidewalk. If the angle of elevation from the tip of the shadow to the sun is 60°, what is the distance from the tip of the shadow to the top of his head? (round to 2 decimal places)

A) 5.50 feet

B) 6.35 feet

C) 6.47 feet

D) 7.00 feet

E) 9.52 feet

If r and s are odd positive integers. Which expression must also be an odd integer?

A) 3rs

B) r + 3s

C) 3r - s

D) (rs + 3)^2

E) 3r^2 + 3s^2

Find the length of the segment with endpoints of (3, 2) and (-3, -6).

A) 100

B) 10

C) 4

D) √(28)  ≈ 5.29

E) √(90)  ≈ 9.49

Oct 19, 2019

#1
+2

#1

Right angle triangle, Adam's height is equal to one of its side (Opposite to angle 60)

So,

Using trigonometry

we know that sin(60)=opp/hyp (We want to find the hypotenuse as it will tell us the distance from the tip of the shadow to the real adam's head.

(Angle 60 is at the tip of the shadow)

sin(60)=5.6/x (x is the hypotenuse)

xsin(60)=5.6

Now divide each side by sin(60)

x=5.6/sin(60)=6.46632301 approx.=6.47 Option c is correct.

#2

"

"If r and s are odd positive integers. Which expression must also be an odd integer?"

Just let r=1 , s=3 (Or any other odd positive integer)

First, 3rs , 3(1)(3)=9 (Which is odd so A is the correct choice) If you tried all, all are wrong except A

#3

Graph it, then make a line going from up to down till it touches the same horizontal line as the other endpoint, and match it straightly.

Other method (Imo better)

(3-(-3))^2 + (2-(-6))^2

= 6^2+8^2= 36+64=100

sqrt(100)=10

Oct 19, 2019

#1
+2

#1

Right angle triangle, Adam's height is equal to one of its side (Opposite to angle 60)

So,

Using trigonometry

we know that sin(60)=opp/hyp (We want to find the hypotenuse as it will tell us the distance from the tip of the shadow to the real adam's head.

(Angle 60 is at the tip of the shadow)

sin(60)=5.6/x (x is the hypotenuse)

xsin(60)=5.6

Now divide each side by sin(60)

x=5.6/sin(60)=6.46632301 approx.=6.47 Option c is correct.

#2

"

"If r and s are odd positive integers. Which expression must also be an odd integer?"

Just let r=1 , s=3 (Or any other odd positive integer)

First, 3rs , 3(1)(3)=9 (Which is odd so A is the correct choice) If you tried all, all are wrong except A

#3

Graph it, then make a line going from up to down till it touches the same horizontal line as the other endpoint, and match it straightly.

Other method (Imo better)

(3-(-3))^2 + (2-(-6))^2

= 6^2+8^2= 36+64=100

sqrt(100)=10

Guest Oct 19, 2019
#2
+1

1. it was B

macabresubwoofer  Oct 19, 2019
#4
+1

Oh sorry, i calculated it wrong (Calculator lol) But the metho is correct as Cphil did :)

Guest Oct 19, 2019
#3
+2

1)  5 ft 6 in  =   5.5 ft

We know the opposite side to  the given angle and we are looking for the hypotenuse

So.....the sine is what we need

sin 60°   =  5.5  / hypotenuse        rearrange as

hypotenuse  =   5.5  / sin (60)   =   6.35 ft   Oct 19, 2019