Question

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

Answer 1

DL = 5.87 un.

LN = 10.98 un.

DN = 14.4 un.

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=(DF)/(\cos \angle D)\\ \\DL=(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=(LF)/(\sin \angle N)\\ \\LN=(4.29)/(\sin 23^(\circ))\approx 10.98\ units`

Hence,

DN = 4.29 + 10.11 = 14.4 units