Question

13)Given triangle XYZ as shown at right find YZ rounded to the nearest tenth

Answer 1

Part 3) Given triangle XYZ as shown at right find YZ rounded to the nearest tenth

we know that
the sum of the internal angles of a triangle add up to 180 degrees
so
m∠X=180-[55+29]----> 96°
applying the law of sines
YZ/sin X=35/sin 55°------> YZ=35*sin 96/sin 55-----> YZ=42.49
YZ=42.5 units

the answer Part 3) is
YZ=42.5 units

Part 4)
we know that
OQ/NQ=PR/NR
NQ=4X+(2X+2)---> 6X+2
OQ=2X+2
PR=15
NR=24+15----> 39
(2X+2)/(6X+2)=15/39
39*(2X+2)=15*(6X+2)
78X+78=90X+30
90X-78X=78-30
12X=48
X=4

The answer part 4) is
x=4

Part 5) A trapezoid  is show below. Calculate the measure of angle x. Round to the nearest tenth of a degree

see the picture with letters attached to better understand the problem

we know that
BC=36-28-----> 8 ft

sin x=BC/AC-----> sin x=8/12
x=arc sin(8/12)-------> x=41.81°------> x=41.8°

the answer Part 5) is
x=41.8°