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STALIN [3.7K]
3 years ago
12

WILL MARK BRAINLIEST! PLEASE HELP

Mathematics
1 answer:
zmey [24]3 years ago
4 0
Part 1) <span>In triangle PQR, mP= 43, PQ=7.5 and PR= 8.4. What is mR to the nearest degree?

we know that
the law of cosines establishes that
c</span>²=a²+b²-2*a*b*cos C

in this problem

c=QR
a=PQ=7.5
b=PR=8.4
C=angle P=43°
c²=a²+b²-2*a*b*cos C----> c²=7.5²+8.4²-2*7.5*8.4*cos 43°
c²=34.66--------> c=5.89
QR=5.9 

applying the law of sines
7.5/sin R=5.9/sin 43-----> 7.5*sin 43=5.9*sin R---> sin R=7.5*sin 43/5.9
sin R=0.8669---------> R=arc sin (0.8669)----> R=60.11°----> R=60°

the answer Part 1) is the option
<span>D. 60
</span>
Part 2) <span>In triangle ABC mA=43, mB=62 and BC=22 in. What is AB to the nearest tenth of an inch?

we know that 
</span>∠C=180-(62+43)-----> ∠C=75°
<span>
Applying the law of sines
22/sin 43=AB/sin 75------> AB=22*sin 75/ sin 43-----> AB=31.16 in
AB=31.2 in

the answer Part 2) is
</span><span>D.31.2</span>
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