Question

Find the missing side

Answer 1

x ≈ 19.6

Explanation:

Since the triangle is right use the cosine ratio to solve for x

cos35° =
`(adjacent)/(hypotenuse)` =
`(x)/(19)`

Multiply both sides by 19

19 × cos35° = x, hence

x ≈ 19.6 ( to 1 dec. place )

Answer 2

`x=15.56`

Explanation:

We can use the law of sines here. However, we will first need to solve for the missing angle.

The interior angles of a triangle add up to 180.

Therefore,

`35+90+x=180`

where
`x` is the missing angle.

`35+90+x=180`

`x+125=180`

`x=55`

So the missing angle is 55 degrees.

Now we can use the law of sines to set up a proportion.

`(19)/(sin(90))=(x)/(sin(55))`

Now simplify the equation.

`x=15.56`

Rounded to the nearest hundredth.