Question

Find y.
Round to the nearest tenth:
у
270
350 ft
y = [? ]ft

Answer 1

178.3

Explanation:

Hello There!

We can find the value of y using trigonometry

These are the trigonometric ratios

Remember SOHCAHTOA

Sine = Opposite over Hypotenuse

Cosine = Adjacent over Hypotenuse

Tangent = Opposite over Adjacent

For the angle that has a measure of 27 degrees

we are given its adjacent angle and we need to find its opposite angle (y)

Adjacent and Opposite sides corresponds with the trigonometric ratio Tangent so we are going to use the trigonometric ratio tan to solve for y

Now we set up an equation (remember tangent = opposite over adjacent)

`tan(27)=(y)/(350)`

Now that we have created an equation we want to solve for y

What we want to do is isolate the variable using inverse operations

So basically we want to get rid of the 350

The opposite of division is multiplication so we multiply each side by 350 to get rid of it

`tan(27)*350=350tan(27)\\(y)/(350) *350=y\\y=350tan(27)\\350tan(27)=178.3339073\\`

so we can conclude that y = 178.3339073

finally we want to round to the nearest tenth and we get that the answer is 178.3