Question

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

Answer 1

For the given triangle, DE = 6.97 units.

Step-by-step 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.

$cos \theta = \frac{adjacentside}{hypotenuse}.$

Step 2:

The length of the adjacent side = 4 units.

The length of the hypotenuse = x units.

The angle of the triangle = 55°.

$cos \theta = \frac{adjacentside}{hypotenuse}, cos 55 = \frac{4}{x}, cos 55 = 0.5735.$

$x = \frac{4}{0.5735} = 6.9747.$

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