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2 years ago

Sophia wants to solve for the side length of b. Which equation could Sophia use to solve for the side length of b, given the

Mathematics

1 answer:

Afina-wow [57]2 years ago

3 0

Answer:

b² = a² + c² - 2ac cos B

Step-by-step explanation:

The cosine rule can be use when you are given three sides of a triangle and ask to find any angle or when you are given two sides and a included angles(the angle between the two sides given) and ask to find the length of a side.

The equation Sophia can use to solve for the side length(b) of a triangle when given two length and the included angle can be expressed below. Sophia was given two sides and an included angle and was asked to find a side length b.

For sides a, b and c the cosine rule can be represented below

a² = b² + c² - 2bc cos A

b² = a² + c² - 2ac cos B

c² = a² + b² - 2ab cos C

The equation required base on your question is

b² = a² + c² - 2ac cos B

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makkiz [27]

Answer:

$\frac{\sqrt{41}}{4}$

Step-by-step explanation:

sec(theta) is defined as: $sec(\theta)=\frac{1}{cos(\theta)} = \frac{hypotenuse}{adjacent}$

In the diagram you provided the hypotenuse of the triangle is sqrt(41) and the opposite side is 5, using these two sides, we can solve for the adjacent side by using the Pythagorean Theorem: $a^2+b^2=c^2$

So this gives us the equation where a=adjacent side:

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