Question

Find the length DE. Round your answer to the nearest tenth of a meter

Answer 1

Answer:

13.8

Step-by-step explanation:

We can use trigonometry to find the length of DE

Remember these are the trigonometric ratios

Sin = Opposite over Hypotenuse

Cos = Adjacent over Hypotenuse

Tan = Opposite over Adjacent

For ∠FDE we are given its opposite side length ( FE ) and need to find its adjacent angle ( DE )

When working with opposite and adjacent we use the trig ratio tangent

That being said we want to create an equation to solve for (DE) ( Recall that tan = opposite over adjacent. ) ( let DE = x )

so $tan(51)=\frac{17}{x}$

now we solve for x

Step 1 multiply each side by x

tan(51) * x = x tan (51)

$\frac{17}{x} *x=17$

now we have x tan (51) = 17

step 2 divide each side by tan (51)

$\frac{xtan(51)}{tan(51)}=x\\\frac{17}{tan(51)}$

we now have

$x =\frac{17}{tan(51)}$

$tan(51)=1.234897157\\\frac{17}{1.234897157} =13.76632856$

we're left with x = 13.76632856

Finally we round to the nearest tenth and get that the answer 13.8