On a piece of paper, use a protractor to construct right triangle ABC with AB=3 in. , m∠A=90° , and m∠B=45° .

What statement is true about the triangle?

AC=3 in.

BC=3 in.

BC=6 in.

AC=6 in.

Option A: is true about the triangle.

Explanation:

The measurements of the right triangle ABC is , and

The image of the triangle having these measurements is attached below:

Option A:

Using Pythagorean theorem, we have,

Thus, the length of AC is

Therefore, Option A is true about the triangle.

Hence, Option A is the correct answer.

Option B:

Using Pythagorean theorem, we have,

Thus, the length of BC is

Therefore, Option B is not true about the triangle.

Hence, Option B is not the correct answer.

Option C:

Using Pythagorean theorem, we have,

Thus, the length of BC is

Therefore, Option C is not true about the triangle.

Hence, Option C is not the correct answer.

Option D:

Using Pythagorean theorem, we have,

Thus, the length of AC is

Therefore, Option D is not true about the triangle.

Hence, Option D is not the correct answer.

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)