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>
The answer should be y=9 and y=-11
<span><span> x = 7/5 = 1.400
</span><span> x = 0 </span></span>
We can use PEMDAS to help us:
P - Parenthesis
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
PEMDAS states what occurs first in order of which letter pertains to which mathematical operation and how you are suppose to do it from left to right. Since multiplication and division comes before addition and subtraction, we know C isn't the answer since it is subtraction. This leaves us with A, B, and D. They all happen to be either multiplication and division. Although multiplication SEEMS to come before division, multiplication and division are actually paired together (just like addition and subtraction) meaning that if either a multiplication or division comes before a division and multiplication operation, you do it left to right. For example, 2 x 2/2. You do 2 x 2 first equaling 4 and then divide by 2 to get 2. Another example is 10/2 x 5. You DO NOT do multiplication first since multiplication and division are paired together meaning you do 10/2 equaling 5 and then do 5 x 5 equaling 25. Enough explanation for that part. Since 20/4 is the first multiplication/division operation, that is what you do first. The answer is A.
