Answer:
11) 9
12)10.27
13)4.05
14)8.1
Step-by-step explanation:
In Δ LMN
angle N = 90 degrees, angle L = 45 degrees
The sum of measures of a triangle is 180 degrees.
45 + 90 + angle M = 180
angle M = 180 - (90+45)
angle M = 45 degrees
This goes under 45 - 45 - 90 degree theorem,
therefore, This is an isoceles triangle.
Therefore the two adjacent sides would be equal.
11) LN = MN
if LN = 9
then, MN = 9
This goes under 45 - 45 - 90 degree theorem,
12) LM = 1/√2 * LM ............(hypotenuse)
9 = 1/√2 * LM
LM = 9 * √2
LM = 9 * 1.414. ........(as value of √2 is 1.414)
therefore, LM = 10.27
In Δ OPQ
angle Q = 90 degrees, angle P = 60 degrees
The sum of measures of a triangle is 180 degrees.
60+ 90 + angle O = 180
angle O = 180 - (60 + 90)
angle O = 30 degrees
This goes under 30 - 60 - 90 degree theorem,
14) side opposite to 60 degree is OQ,
OQ = √3/ 2 * OP
7 = √3 / 2 * OP
OP = 7* 2 / √3
OP = 14/ √3
OP = 8.1
13) This goes under 30 - 60 - 90 degree theorem,
side opposite to 30 degrees is PQ,
PQ = 1/2 * OP
PQ = 1/2 * 8.1
= 4.05
