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3 years ago

Help please . Thank you !!

Mathematics

1 answer:

dmitriy555 [2]3 years ago

4 0

Answer:

A=25m

Step-by-step explanation:

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Answer:

D. a = 11.71 and b = 15.56

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Trigonometry

All angles in a triangle add up to 180°

Pre-Calculus

Law of Sines: $\frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}$

Step-by-step explanation:

Step 1: Define

AC = b

CB = a

AB = 7

m∠A = 45°

m∠B = 110°

m∠C = ?

Step 2: Find missing ∠

Set up equation: m∠C + 45° + 110° = 180°
Combine like terms: m∠C + 115° = 180°
Isolate unknown: m∠C = 25°

Step 3: Find measure of b

Substitute: $\frac{sin(25)}{7} =\frac{sin(110)}{b}$
Cross-multiply: $bsin(25)=7sin(110)$
Isolate b: $b=\frac{7sin(110)}{sin(25)}$
Evaluate: $b=15.5645$
Round: $b \approx 15.56$

Step 4: Find measure of a

Substitute: $\frac{sin(25)}{7} =\frac{sin(45)}{a}$
Cross-multiply: $asin(25)=7sin(45)$
Isolate a: $a=\frac{7sin(45)}{sin(25)}$
Evaluate: $a=11.7121$
Round: $a \approx 11.71$

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