Question

Select the angle that correctly completes the law of cosines for this triangle.

Answer 1

Answer:

Option C. 74°

Step-by-step explanation:

we know that

The law of cosines formula is equal to

$a^{2} =b^2+c^2-2(b)(c)cos(A)$

where

The angle A is the opposite angle to side a

In this problem

Let

$a=24\ units\\b=7\ units\\c=25\ units\\A=74\°\\B=6\°\\C=90\°$

substitute in the formula

$24^{2} =7^2+25^2-2(7)(25)cos(74\°)$

Answer 2

The angle that correctly completes the law of cosines for this triangle is 74°

Further explanation

Firstly , let us learn about trigonometry in mathematics.

Suppose the ΔABC is a right triangle and ∠A is 90°.

sin ∠A = opposite / hypotenuse

cos ∠A = adjacent / hypotenuse

tan ∠A = opposite / adjacent

Let us now tackle the problem!

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In this problem, we will use the law of cosines as follows:

$a^2 = b^2 + c^2 - 2bc \cos \theta$

where:

θ is the angle between the sides of b and c.

a is the opposite side of θ.

$\texttt{ }$

Based on the rules above, it can be written down:

$24^2 = 7^2 + 25^2 - 2(7)(25) \cos \boxed{74^o}$

The angle that correctly completes the law of cosines for this triangle is $\boxed{74^o}$

Another law of cosines could be written as follows:

$7^2 = 24^2 + 25^2 - 2(24)(25) \cos \boxed{6^o}$

$25^2 = 7^2 + 24^2 - 2(7)(24) \cos \boxed{90^o}$

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Learn more

• Calculate Angle in Triangle : brainly.com/question/12438587
• Periodic Functions and Trigonometry : brainly.com/question/9718382
• Trigonometry Formula : brainly.com/question/12668178

Answer details

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle