Solve the triangle. A = 19°, C = 102°, c = 6

1 answer:

7 0

We know that

Law of sines established
a/sin A=b/sin B=c/sin C

then
a/sin A=c/sin C------------> a=c*sin A/sin C---------> a=6*sin 19/sin 102
a=1.91 units ≈2 units

A+B+C=180°----------> B=180-(A+C)-----> B=1180-(19+102)
B=59°
a/sin A=b/sin B-----------> b=a*sin B/sin A----->2*sin 59/sin 19
b=5.27 units ≈5.3 units

the answer is the option
B = 59°, a ≈ 2, b ≈ 5.3

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(iii) Find the smallest whole number h such that 4704/h is a cube number.

yan [13]

Answer:

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Step-by-step explanation:

Given the fraction $\dfrac{4,704}{h}$

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$4,704=2^5\cdot 3\cdot 7^2$

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Using sin rule:
a/sin A =b/sin B=c/sin c
SIN A=sin 46=0.72
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then B= 34°
AS the sum of triangle angles=180
then C=180-(46+34)=100°
then c =(a*sin C)/sin A
sin C=sin 100=0.98
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3 years ago

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Match the following STATEMENTS to the reasons listed. NOTE: In a traditional proof format, the statements would be on the left s

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1. RM = SN, TM = TN Addition Property of Equality

2. ∠T = ∠T Reflexive

3. RM + TM = SN + TN Substitution

4. RM + TM = RT, SN + TN = ST Betweeness

5. RT = ST CPCTE

6. Triangle RTN congruent to Triangle STM Given

7. RN = SM SAS