Question

After Jeremy runs across the width of the building, he must run down a ramp to the next building. Use the following portion of the picture to set up a ratio.

a.sin=70 =(4/x)
b. cos70 = (4/x)
c. cos 70 =(x/4)
d. sin 70 = (x/4)

Answer 1

`b.\ cos 70 =\frac{4}x` is the correct answer.

Explanation:

First of all, let us label the diagram as shown in the attached figure.

OR = 20'

QS = 16'

`\triangle OPQ` is the right angled triangle that we get.

`\angle P=90^\circ`

`\angle O =70^\circ`

From the given figure symmetry, we can clearly see that:

Side OP = OR - QS

OP = 20 - 16 = 4'

Now, let us use trigonometric identity of cosine in
`\triangle OPQ`.

`cos\theta = (Base)/(Hypotenuse)`

`cosO= (OP)/(OQ)\\\Rightarrow cos70^\circ= (4)/(OQ)`

Let the distance of ramp, OQ = x'

So, the above ratio becomes:

`cos70^\circ= (4)/(x)`

So, the correct answer is:

`b.\ cos 70 =\frac{4}x`