Question

Solve for x. Round your answer to 2 decimal places.

A right triangle is shown where the angle between the hypotenuse, of length x units, and a leg, of length eighteen units, is fifty degrees.

Answer 1

You'll solve using trig identities. We have the adjacent leg length and we want the hypotenuse length. Thus, we will use the cosine identity

cos angle = adjacent / hypotenuse

Using the information in the problem, we have :

cos 50 = 18 / hypotenuse

x = hypotenuse = 18 / cos 50

Answer 2

28.00 units.

Explanation:

We have been given that a the angle between the hypotenuse of a right triangle, of length x units, and a leg, of length eighteen units, is fifty degrees. We are asked to find the value of x.

The given information tells us that side with length of 18 units is adjacent side to angle 50 degrees.

We know that cosine relates adjacent side of right triangle to hypotenuse. We can represent our given information in an equation as:

`\text{cos}(50^(\circ))=(18)/(x)`

`x=\frac{18}{\text{cos}(50^(\circ))}`

`x=(18)/(0.642787609687)`

`x=28.003028\approx 28.00`

Therefore, the hypotenuse of given triangle would be 28.00 units.