3 years ago

In triangle ABC shown, DE || AC. What is the length of AC?

Mathematics

2 answers:

aliina [53]3 years ago

7 0

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Aliun [14]3 years ago

4 0

Answer:

AC = 20

Step-by-step explanation:

Δ BDE and Δ BAC are similar, so the ratios of corresponding sides are equal, that is

$\frac{AC}{DE}$ = $\frac{BA}{BD}$ , substitute values

$\frac{AC}{8}$ = $\frac{10}{4}$ ( cross- multiply )

4AC = 80 ( divide both sides by 4 )

AC = 20

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Which equation correctly uses the law of cosines to solve for the missing side length of trianglepqr? 62 = p2 82 – 2(p)(8)cos(39

Evgesh-ka [11]

The equation that correctly uses the law of cosines to solve for the missing side length of trianglepqr is <u>8^2 = 7^2 +11^2 - 2(7)(11) cos <P</u>

<h3>The cosine rule formula</h3>

For us to use the cosine formula, an angle must be situated between two sides of the triangle.

According to the rule;

c^2 = a^2 + b^2 - 2ab cos C

From the given diagram, if cos<P is the reference angle, then;

a = 11

b = 7

c = 8

Substiute

8^2 = 7^2 +11^2 - 2(7)(11) cos <P

Hence the equation that correctly uses the law of cosines to solve for the missing side length of trianglepqr is <u>8^2 = 7^2 +11^2 - 2(7)(11) cos <P</u>

Learn more on law of cosine here: brainly.com/question/8288607