Question

In DEF, FE=13 and m(angle)F=34. Find DF to the nearest tenth

Answer 1

A.15.7
is the answer because fe is 13

Answer 2

DF is 15.7 unit

Explanation:

Given,

In triangle DEF,

m∠E = 90°, m∠F = 34° and EF = 13,

We have to find the measure of side DF.

By the property of a triangle,

m∠E + m∠F + m∠D = 180°

⇒ 90° + 34° + m∠D = 180°

⇒ m∠D = 180° - 124° = 56°

By the law of sines,

`(sin D)/(EF)=(sin E)/(DF)`

`sin D* DF = sin E* EF` ( By cross multiplication )

`\implies DF = ( sin E* EF)/(sin D)`

By substituting values,

`DF = (sin 90^(\circ)* 13)/(sin 56^(\circ))=15.6808333306\approx 15.7\text{ unit}`