Question

Given ADEF, find DE.
Round your answer to the nearest hundredth.
55
Check

Answer 1

For the given triangle, DE = 6.97 units.

Explanation:

Step 1:

In the given triangle, the angle is 55°. The adjacent side has a length of 4 units and assume the hypotenuse, DE measures x units.

To calculate the value of x, we determine the cos of the triangle where we divide the length of the adjacent side by the length of the hypotenuse.

`cos \theta = (adjacentside)/(hypotenuse).`

Step 2:

The length of the adjacent side = 4 units.

The length of the hypotenuse = x units.

The angle of the triangle = 55°.

`cos \theta = (adjacentside)/(hypotenuse), cos 55 = (4)/(x), cos 55 = 0.5735.`

`x = (4)/(0.5735) = 6.9747.`

So x = DE = 6.9747 units, rounding this off to the nearest hundredth we get DE = 6.97 units.