Mathematics, 25.03.2020 04:25 DineroLaForeign

Which equations could be used to solve for the
unknown lengths of AABC? Check all that apply.

Which equations could be used to solve for the unknown lengths of AABC? Check all that apply.

Answers: 2

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Answer from: joanasprinkman2262

Given that ABC is a right triangle.

The measure of ∠A is 45° and AB = 9

We need to determine the equations that could be used to solve the unknown lengths of ΔABC

Option A: $\sin \left(45^{\circ}\right)=\frac{BC}{9}$

The length of BC can be determined using the trigonometric ratios.

$sin\ \theta=\frac{opp}{hyp}$

where $\theta=45^{\circ}$ , opp= BC and hyp = 9

Hence, substituting the values, we get;

$\sin \left(45^{\circ}\right)=\frac{BC}{9}$

Hence, Option A is the correct answer.

Option B: $\sin \left(45^{\circ}\right)=\frac{9}{BC}$

The length of BC can be determined using the trigonometric ratios.

$sin\ \theta=\frac{opp}{hyp}$

where $\theta=45^{\circ}$ , opp= BC and hyp = 9

Hence, substituting the values, we get;

$\sin \left(45^{\circ}\right)=\frac{BC}{9}$

Thus, the length of BC can be determined using $\sin \left(45^{\circ}\right)=\frac{BC}{9}$

Hence, Option B is not the correct answer.

Option C: $9 \tan \left(45^{\circ}\right)=A C$

The length of AC can be determined using the trigonometric ratios.

$tan \ \theta= \frac{opp}{adj}$

where $\theta=45^{\circ}$ , opp= BC and adj=AC

Substituting the values, we get;

$tan \ 45^{\circ}=\frac{BC}{AC}$

Thus, the length of AC using the trigonometric ratios is $tan \ 45^{\circ}=\frac{BC}{AC}$

Hence, Option C is not the correct answer.

Option D: $(A C) \sin \left(45^{\circ}\right)=B C$

The formula for $sin \ \theta$ is given by the formula,

$sin\ \theta=\frac{opp}{hyp}$

where $\theta=45^{\circ}$ , opp= BC and hyp = 9

Hence, substituting the values, we get;

$\sin \left(45^{\circ}\right)=\frac{BC}{9}$

Thus, the given equation $(A C) \sin \left(45^{\circ}\right)=B C$ is wrong.

Hence, Option D is not the correct answer.

Option E: $\cos \left(45^{\circ}\right)=\frac{BC}{9}$

The formula for $cos \ \theta$ is given by the formula,

$cos \ \theta=\frac{adj}{hyp}$

where $\theta=45^{\circ}$ , adj=AC and hyp = 9

Substituting the values, we get;

$\cos \left(45^{\circ}\right)=\frac{AC}{9}$

Hence, the given equation $\cos \left(45^{\circ}\right)=\frac{BC}{9}$ is not possible.

Thus, Option E is not the correct answer.

Answer from: Quest

Ithink it’s d as the answer.

Answer from: Quest

statement #3: proof- ang is congruent to ang ecd : angles are congruent.

step-by-step explanation:

1: the missing angles in statement #3

a.) acb

reason- the reason why the answer is acb is because angle ecd and angle acb are both the same size *that's what the word congruent means this is really simple.

2: the missing word in reason #3

c.) vertical

reason- the reason why the answer is vertical is because the angles in that diagram on figure 2 is slanted, which is vertical, and the e and a both lay on vertical lines. along with the other's, but e and a are the 2 main points you want to focus on. and c is kind of like your starting point, because c is for both angles, not just one.

i hope that was and understanding.

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