3. Priya says, "I know everything about a right triangle with a 30 degree angle and a hypotenuse with length 1 cm. Here look." The other angle is 60 degrees. The leg adjacent to the 30 degree angle 0.866 cm long. The side opposite the 30 degree angle is 0.5 cm long. Han asks, "What would happen if a right triangle with a 30 degree angle has a hypotenuse that is 2 cm instead?" Help them find the missing angles and side lengths in the new triangle. Explain or show your reasoning.

1) The measure of the third angle is 60°

2) The length of the opposite side to the angle 30° is 1 cm

3) The length of the opposite side to the third angle 60° is approximately 1.732 cm

Step-by-step explanation:

1) The given parameters are;

The known angle of a right triangle = 30°

The length of the hypotenuse = 2 cm

Given that the triangle = A right triangle, with one of the interior angles = 90°, we have;

The measure of the third angle = 180° - 90° - 30° = 60°

The measure of the third angle = 60°

2) We have that sin(30°) = 0.5 = (The length of the opposite side to the angle 30°)/(The length of the hypotenuse side)

0.5 = (The length of the opposite side to the angle 30°)/(2 cm)

∴ The length of the opposite side to the angle 30° = 2 cm × 0.5 = 1 cm

The length of the opposite side to the angle 30° = 1 cm

3) Similarly, the length of the opposite side to the third angle 60° = sin(60°) × (The length of the hypotenuse side)

∴ The length of the opposite side to the third angle 60° = (√3)/2 × 2 cm = √3 cm

The length of the opposite side to the third angle 60°  = √3 cm ≈ 1.732 cm

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

a. 32 degrees

step-by-step explanation:

here we have to use the rule.

m∠e = 1/2 (major arc - minor arc)

m∠e = 1/2 (212 - 148)

m∠e = 1/2 (64)

m∠e = 32 degrees

answer: a. 32 degrees

you