Question

In △ABC,a=13, b=14, and c=18. Find m∠A.

Answer 1

Answer:

m∠A = 45.86°

Step-by-step explanation:

A rough sketch of the triangle is shown in the attached pic.

When 3 sides are given and we want to solve for an angle, we use the Cosine Rule. Which is:

$p^2=a^2 +b^2 -2abCosP$

Where a, b, p are the lengths of 3 sides (with p being the side opposite of the angle we are solving for) and P is the angel we want to solve for

Thus, we have:

$p^2=a^2 +b^2 -2abCosP\\13^2=14^2 +18^2-2(14)(18)CosA\\169=520-504CosA\\504CosA=351\\CosA=\frac{351}{504}\\CosA=0.6964\\A=Cos^{-1}(0.6964)=45.86$

Answer 2

In △ABC,a=13, b=14, and c=18. Then angle, m∠A is is 46.654°

Further Explanation;

• In a triangle ΔABC, with sides a, b, and c, and angles ∠A, ∠B, and ∠C can be solved using sine rule or cosine rule.

Sine rule

• This rule is used when one is given two sides of the triangle and an angle, or one side and two angles are known.
• According top sine rule;

$\frac{a}{sinA}=\frac{b}{sinB} =\frac{c}{sinC}$

Cosine rule

• Cosine rule is used when all the sides of the triangle are known or when two sides of a traingle and an angle are known.
• According to cosine rule;

$a^{2} =b^{2} +c^{2} -2bcCosA$ or

$b^{2} =a^{2} +c^{2} -2acCosB$ or

$c^{2} =a^{2} +b^{2} -2abCosC$

In our case;

we are going to use Cosine rule to find m∠A

We are given;

a=13, b=14, and c=18

Therefore;

$a^{2} =b^{2} +c^{2} -2bcCosA$

Replacing the variables;

$13^{2} =14^{2} +18^{2} -2(14)(18)CosA$

Making CosA the subject;

$CosA = \frac{(13^{2} -14^{2} -18^{2})}{-2(14)(18)}$

$Cos A = \frac{-351}{-504}$

$CosA = 0.6964$

$A = Cos^{-1} (0.6864)$

$A = 46.654$

Therefore; In △ABC,a=13, b=14, and c=18, m∠A is 46.654°

Keywords: Sine rule, Cosine rule

Learn more about:

• Sine rule: brainly.com/question/10657743
• Example on sine rule; brainly.com/question/10657743
• Cosine rule: brainly.com/question/3137169
• Example on cosine rule; brainly.com/question/12241039

Level; High school

Subject: Mathematics

Topic: Triangles

Sub-topic: Cosine and sine rule