Question

A 45 foot long escalator rises from the first floor to the second floor of a shopping mall. The escalator makes a 30° angle with the horizontal. How high above the first floor is the second floor?

Answer 1

A. 26 ft
B. 78 ft
C. 22.5 ft
D. 45 ft

Answer 2

So we have an angle, and the hypotenuse, and we want the opposite side from the angle

Which trig function uses opposite and hypotenuse?

Answer 3

huh?

Answer 4

Hmm what grade of math are you in?

Answer 5

10th grade geometry

Answer 6

Oh okay, then we'll use the special triangles way (sorry I was doing trigonometry before)

Answer 7

it's okay.

Answer 8

its a 30, 60, 90

Answer 9

So what we have is a 30-60-90 triangle

the side ratios that we have with that type of triangle is



So the side opposite the 30 degree angle, is our shortest leg,
The side opposite the right angle, is 2 times what that length will be

Since we know that long side to be 45..we know the side opposite the 30 degree angle will be half the 45......

\[\large \frac{45}{2} = 22.5\]

Answer 10

Omg i was right yay!

Answer 11

I was just double checkiung

Answer 12

Haha great job :)

Answer 13

can u help me double check like 3 more

Answer 14

Lol sure :)

Answer 15

A ladder 15 feet long leans against a wall and forms an angle of 45º with the ground. How far from the wall is the ladder?
A. 15 ft
B. 7.5 ft
C. square root of 2
D. 7.5 square root of 2

Answer 16

And what did you get :P

Answer 17

7.5

Answer 18

7.5 square root of 2...close :)

Answer 19

yay

Answer 20

Because that time, the side ratios are



So we have the side that relates to the √2

To figure out the other side...we need (what number times √2 = 15 ??

So

\[\large x√2 = 15\]

\[\large x = \frac{15}{\sqrt{2}}\]
\[\large x = \frac{15\sqrt{2}}{2}\]
\[\large x = 7.5\sqrt{2}\]