Question

Given: ∆DLN, LF ⊥ DN , DF = 4 m∠N = 23º, m∠D = 47º Find: DL, LN, DN

Answer 1

Answer:

DL = 5.87 un.

LN = 10.98 un.

DN = 14.4 un.

Step-by-step explanation:

Given:

∆DLN,

LF ⊥ DN ,

DF = 4

m∠N = 23º,

m∠D = 47º

Find:

DL, LN, DN

Solution:

In right triangle DFL, DF = 4, m∠D = 47º, so

$LF=DF\tan \angle D\\ \\LF=4\cdot \tan 47^{\circ}\approx 4.29 \ units$

and

$DL=\dfrac{DF}{\cos \angle D}\\ \\DL=\dfrac{4}{\cos 47^{\circ}}\approx 5.87\ units$

In right triangle LFN, LF = 4.29 units,  m∠N = 23º, so

$FN=LF\cot \angle N\\ \\FN=4.29\cdot \cot 23^{\circ}\approx 10.11\ units$

and

$LN=\dfrac{LF}{\sin \angle N}\\ \\LN=\dfrac{4.29}{\sin 23^{\circ}}\approx 10.98\ units$

Hence,

DN = 4.29 + 10.11 = 14.4 units