Question

Quick ASAP What is the length of the hypotenuse in triangleDEF? Round to the nearest tenth?

Answer 1

Check the picture below.

`\cos(41^o )=\cfrac{\stackrel{adjacent}{4}}{\underset{hypotenuse}{h}} \implies h\cos(41^o)=4\implies h=\cfrac{4}{\cos(41^o)}\implies h\approx 5.3`

Make sure your calculator is in Degree mode.

Answer 2

5.3

Explanation:

For the given angle D, 4 is the adjacent leg.

The hypotenuse is DE.

The trigonometric ratio that relates the adjacent leg to the hypotenuse is the cosine ratio.

In general,

cos A = adj/hyp

In this case,

cos D = adj/hyp

cos 41° = DF/DE

cos 41° = 4/DE

(DE)(cos 41°) = 4

DE = 4/(cos 41°)

DE = 4/0.75470958 <----- value of cosine obtained from calculator

DE = 5.3