Question

eric leans a ladder against the roof of his house so that the ladder forms a 70 degree angle with the ground. the roof of the house is 13 feet above the ground. how far is the bottom of the ladder from the base of the house? round the answer to the nearest tenth.
a. 0.2 feet
b. 4.4 feet
c. 4.7 feet
d. 71.2 feet

Answer 1

@pitamar

Answer 2

ANYONE PLLZZZ HELP!!!

Answer 3

hmm, forgot to draw 90 degrees angle there


Can you tell me what will be the \(\frac{13}{x}\) in the triangle? what trig function can you use to get this ratio?

Answer 4

not sure

Answer 5

ok, if we have a right angle triangle:

with angle alpha (\(\alpha\)), sides a,b and hypotenuse c.
Then
\(\frac{a}{c} = \sin(\alpha)\)

\(\frac{b}{c} = \cos(\alpha)\)

\(\frac{a}{b} = \tan(\alpha)\)

Answer 6

which one is like what we have here?

Answer 7

sin

Answer 8

no, because 13 in our case is like \(a\) in the drawing and \(x\) in our case is like \(b\) in the drawing
So \( \frac{13}{x} = \frac{a}{b} = ?\)

Answer 9

is 70 a or is 70 b??

Answer 10

70 is alpha (\(\alpha\)) the angle

Answer 11

13 divided by 70??

Answer 12

no. let me show you what I mean.
We want to know that \(\frac{13}{x}\) is. we look at the drawing and see:
13 is the side in front of the angle 70. x is the side adjacent to the angle 70.
That is just like \(\frac{a}{b}\) which I know that is \( \tan(\alpha\)).
In my case \(a = 13_{ft} \qquad b=x \qquad \alpha = 70^\circ\) so I get:
$$
\frac{a}{b} = \tan(\alpha) \implies \frac{13_{ft}}{x} = \tan(70^\circ)
$$
Ok so far?

Answer 13

yeaa

Answer 14

i think so

Answer 15

Ok, but we know what \(\tan(70^\circ)\) is. we go to a calculator and type it:
http://www.wolframalpha.com/input/?i=tan%2870+degrees%29
Which is about 2.74
So we say:
$$
\frac{13_{ft}}{x} = 2.74
$$Can you find x?

Answer 16

36.52?

Answer 17

well let's see. to solve x we have to multiply both sides by x and divide by 2.74:
$$
\frac{13_{ft}}{x} = 2.74 \implies 13_{ft} = 2.74 \cdot x \implies x = \frac{13_{ft}}{2.74}
$$what is 13/2.74?

Answer 18

4.7 so its c right???!!!

Answer 19

yep

Answer 20

ty!!

Answer 21

one more