Question

If r=10 and s=31, find R. Round to the nearest tenth.

Answer 1

The correct answer is option c. 17.9°

Explanation:

From the figure we can see that a right angled triangle RST.

Right angled at T

To find the value of R

It is given that,

r=10 and s=31

Tan R = Opposite side/Adjacent side

Tan R = ST/SR = r/s = 10/31 = 0.3225

R = Tan⁻¹(0.3225) = 17.87 ≈ 17.9°

Therefore the correct answer is option c. 17.9°

Answer 2

C. R = 17.9 degrees

Explanation:

We have a rectangle triangle with the adjacent side and the opposite side (neither of which are the hypotenuse).

The relation between those elements is the tangent:

`tan(angle) = (Opposite side)/(Adjacent side)`

So, to isolate the angle, we modify the formula as such:

`angle = arctan((Opposite side)/(Adjacent side)) = arctan((10)/(31)) = arctan(0.3225) = 17.87`

If we round 17.87 degrees to the tenth... we get 17.9 degrees.