Question

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

Answer 1

Answer:

DF is 15.7 unit

Step-by-step 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,

$\frac{sin D}{EF}=\frac{sin E}{DF}$

$sin D\times DF = sin E\times EF$   ( By cross multiplication )

$\implies DF = \frac{ sin E\times EF}{sin D}$

By substituting values,

$DF = \frac{sin 90^{\circ}\times 13}{sin 56^{\circ}}=15.6808333306\approx 15.7\text{ unit}$

Answer 2

A.15.7
 is the answer because fe is 13