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

Answer:

$b.\ cos 70 =\dfrac{4}x$ is the correct answer.

Step-by-step 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 $\triangle OPQ$.

$cos\theta = \dfrac{Base}{Hypotenuse}$

$cosO= \dfrac{OP}{OQ}\\\Rightarrow cos70^\circ= \dfrac{4}{OQ}$

Let the distance of ramp, OQ = x'

So, the above ratio becomes:

$cos70^\circ= \dfrac{4}{x}$

So, the correct answer is:

$b.\ cos 70 =\dfrac{4}x$