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egoroff_w [7]
2 years ago
15

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

Mathematics
1 answer:
shtirl [24]2 years ago
6 0

Answer:

DL = 5.87 un.

LN = 10.98 un.

DN = 14.4 un.

Step-by-step explanation:

<u>Given:</u>

∆DLN,

LF ⊥ DN ,

DF = 4

m∠N = 23º,

m∠D = 47º

<u>Find:</u>

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

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