Question

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

Answer 1

Option A: $A C=3 \ in$ is true about the triangle.

Explanation:

The measurements of the right triangle ABC is $A B=3 \ in$ , $m \angle A=90^{\circ}$ and $\mathrm{m} \angle{B}=45^{\circ}$

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

Option A: $A C=3 \ in$

Using Pythagorean theorem, we have,

$tan \ 45^{\circ}= \frac{AC}{3}$

   $1\times 3= AC$

         $3=AC$

Thus, the length of AC is $A C=3 \ in$

Therefore, Option A is true about the triangle.

Hence, Option A is the correct answer.

Option B: $B C=3\ in$

Using Pythagorean theorem, we have,

$cos \ 45^{\circ}=\frac{3}{BC}$

     $BC=\frac{3}{cos \ 45^{\circ}}$

     $BC=\frac{3}{0.707}$

     $BC=4.24$

Thus, the length of BC is $BC=4.24 \ in$

Therefore, Option B is not true about the triangle.

Hence, Option B is not the correct answer.

Option C: $B C=6\ in$

Using Pythagorean theorem, we have,

$cos \ 45^{\circ}=\frac{3}{BC}$

     $BC=\frac{3}{cos \ 45^{\circ}}$

     $BC=\frac{3}{0.707}$

     $BC=4.24$

Thus, the length of BC is $BC=4.24 \ in$

Therefore, Option C is not true about the triangle.

Hence, Option C is not the correct answer.

Option D: $A C=6\ in$

Using Pythagorean theorem, we have,

$tan \ 45^{\circ}= \frac{AC}{3}$

   $1\times 3= AC$

         $3=AC$

Thus, the length of AC is $A C=3 \ in$

Therefore, Option D is not true about the triangle.

Hence, Option D is not the correct answer.