Question

In ΔLMN, n = 92 inches, ∠N=46° and ∠L=11°. Find the length of l, to the nearest inch.

Answer 1

Answer:

24 inches

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. The types of triangles are scalene triangle, equilateral triangle, right angled triangle and obtuse triangle.

Sine rule states that given a triangle with sides a, b, c and their corresponding angles opposite to the sides as A, B, C. Then:

$\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}$

In triangle LMN:

We can find the length of l using sine rule:

$\frac{l}{sinL}=\frac{n}{sinN} \\\\substituting:\\\\\frac{l}{sin(11)}=\frac{92}{sin(46)} \\\\l=\frac{92}{sin(46)}*sin(11)\\\\k=24\ inches$