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

Quick ASAP What is the length of the hypotenuse in triangleDEF? Round to the nearest-example-1
User Oobayly
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9.0k points

2 Answers

1 vote

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.

Quick ASAP What is the length of the hypotenuse in triangleDEF? Round to the nearest-example-1
User Apalopohapa
by
8.3k points
6 votes

Answer:

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

User Borislav Aymaliev
by
8.9k points
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