Question

Darren designed this triangular shaped entrance, ABC, to a mall.
Which expression can be used to find the distance between the points B and C of the entrance?

Answer 1

A. 15 /cot 65 +15 / sec 25
B. 15 / cot 65 + 15 cot 25
C. 15/ sec 65 + 15 sec 25
D. 15 /cot 65 + 15/cot 25

Answer 2

BC = BD + DC

so you need to find BD and DC

I'll help you find BD

tan(angle) = opp/adj

tan(65) = BD/AD

tan(65) = BD/15

15*tan(65) = BD

BD = 15*tan(65)

Answer 3

Now because there isn't a tangent expression anywhere in the answer choices, but there is a cotangent expression, this means we must say

BD = 15*tan(65)

BD = 15*(1/cot(65) )

BD = 15/cot(65)

Answer 4

Using the fact that tan(x) = 1/cot(x)

Answer 5

How would you find DC?

Answer 6

Do I use the reciproocal form ...

Answer 7

Use whatever form you are familiar with and we'll go from there

Answer 8

hypotenuse over adjacent or adjacent over opposite ..

Answer 9

AD is given to be 15 ft

it is opposite the given angle of 25 degrees

so AD is the opposite side

Answer 10

we want DC, which is the adjacent side

Answer 11

so what trig function uses opposite and adjacent?

Answer 12

cotangent

Answer 13

good,

cot = adj/opp

Answer 14

so

cot(25) = DC/AD

cot(25) = DC/15

15*cot(25) = DC

CD = 15*cot(25)

Answer 15

DC = 15*cot(25) i meant to write

Answer 16

now go back to the breakdown of BC

BC = BD + DC

and plug in what we just found

BC =15/cot(65) + 15*cot(25)

Answer 17

that leave us with choice B or D

Answer 18

How do you know weither to just write it out like that or in fraction from.

Answer 19

there's a slight difference

Answer 20

I just followed the trig definitions and solved for the unknowns

Answer 21

then plugged them back into BC = BD + DC

Answer 22

Thank You. (:

Answer 23

Do you mind to help me with one more questioned I have it worked out just don't know weither to write it out or put it in fraction from ?

Answer 24

sure go ahead and post

tell me what answer you went with

Answer 25

The sail of a boat is in the shape of a right triangle, as shown below
Which expression shows the length, in meters, of the base of the sail?

Answer 26

7 cossec 50 or
7/cossec 50

Answer 27

let x = length of base

csc(50) = hyp/opp

csc(50) = 7/x

x*csc(50) = 7

x = 7/csc(50)

Answer 28

That's not the same as 7*csc(50) because we're multiplying here instead of dividing

Answer 29

So it is in fraction form

Answer 30

yes

Answer 31

thank you lots. I would give you medals but iM not sure how to give them

Answer 32

that's ok, glad to be of help

Answer 33

(: