Question

What is the value of r?
Round your final answer to the nearest whole number.

Answer 1

r = 13

Explanation:

We are given a right angled triangle with one known angle and two side lengths (12 and r) and we are to find the value of r (which is the hypotenuse).

For that, we can use sine.

`sin ( 67.4 ) = \frac {12} {r}`

`0.923 = \frac {12} {r}`

`r = \frac {12} {0.923}`

`r = 12.9`

r ≈ 13

Therefore, the value of r is 13.

Answer 2

r = 13

Explanation:

Hypotenuse is the side opposite to 90 degree angle, so hypotenuse is r.

Also, with respect to the angle given, the side "12" is the opposite.

So we have opposite side to angle and we need hypotenuse. Which trigonometric ratio related opposite with hypotenuse? It is SINE.

So we can write:

`Sin(67.4)=(Opposite)/(Hypotenuse)=(12)/(r)\\rSin(67.4)=12\\r=(12)/(Sin(67.4))\\r=12.99`

Rounded to nearest whole number, r = 13