Step: 1

If d is the length of the hypotenuse in a 30°- 60° - 90° triangle, then the length of the side opposite the 60° angle is d 3 2 .

Step: 2

So, d 3 2 = 93

Step: 3

Correct Answer is : 18 cm.

Step: 1

If S is the length of the leg of a 45° - 45° - 90° triangle, then the length of the hypotenuse is S2 .

Step: 2

So, S2 = 10

Step: 3

S = 1 0 2

Step: 4

S = 1 0 2 2 × 2 = 1 0 2 2 = 52 cm

Correct Answer is : 52 cm.

Step: 1

In a 30^{o} - 60^{o} - 90^{o} triangle,
the length of the shortest side is half of its hypotenuse.

Correct Answer is : shortest side is half of the hypotenuse

Step: 1

The triangle is a 45^{o} - 45^{o} - 90^{o} triangle.

Step: 2

Length of PR = 72 inches.

Step: 3

In a 45^{o} - 45^{o} - 90^{o} triangle, length of hypotenuse is 2 times the length of leg.

Step: 4

In ΔPQR, PQ ¯ and QR ¯ are congruent legs and PR ¯ is the hypotenuse.

Step: 5

PR = PQ2

Step: 6

PQ = P R 2

[Divide each side by 2 .]

Step: 7

PQ = 7 2 2

[Replace PR with 72 .]

Step: 8

PQ = 7 inches

[Simplify.]

Step: 9

Since the lengths of two legs are equal in 45^{o} - 45^{o} - 90^{o} triangle, PQ = QR = 7 inches.

Step: 10

The lengths of PQ ¯ and QR ¯ are 7 inches.

Correct Answer is : 7 inches and 7 inches

Step: 1

In a 45^{o} - 45^{o} - 90^{o} triangle, the lengths of two legs are same and length of hypotenuse is 2 times the length of a leg.

Step: 2

The triangle is a 45^{o} - 45^{o} - 90^{o} triangle.

Correct Answer is : 45^{o} - 45^{o} - 90^{o}

Step: 1

The side lengths of the triangle are 3, 6 and 33 .

Step: 2

6^{2} = 3^{2} + (33 ) ^{2}

[Checking for Pythagorean theorem.]

Step: 3

Since given measures satisfy Pythagorean theorem, they form a right triangle.

Step: 4

Here, the length of hypotenuse is 6 and the length of shorter leg is 3.

Step: 5

Since the length of hypotenuse is twice the length of shorter leg, the sides form a 30^{o} - 60^{o} - 90^{o} triangle.

Correct Answer is : yes

Step: 1

Since two of the angles of the triangle are equal and one of the angle is 90^{o}, the triangle is an isosceles right triangle.

Step: 2

In an isosceles right triangle,the legs have same length and hypotenuse is 2 times its leg.

Step: 3

Step: 4

BC = AB = 5 cm

[Since legs have same lengths in an isosceles right triangle.]

Step: 5

AC = BC × 2 cm = 52 cm

[Substitute BC = 5.]

Step: 6

The missing sides are BC = 5 cm and AC = 52 cm.

Correct Answer is : BC = 5 cm and AC = 52 cm

Step: 1

Let x units be the length of the shorter side.

Step: 2

[30^{o}-60^{o}-90^{o}-triangle theorem.]

Step: 3

Area of the triangle = (1 2 ) × base × height

[Formula.]

Step: 4

73 = 1 2 × x × x 3

[Substitute.]

Step: 5

[Simplify.]

Step: 6

[Take square root on both sides.]

Step: 7

Length of the shorter leg is 3.74 units.

Correct Answer is : 3.74 units

Step: 1

Let x can be the length of the leg

Step: 2

[45^{o}-45^{o}-90^{o} Triangle Theorem.]

Step: 3

Area of the triangle = 1 2 × base × height

[Formula.]

Step: 4

8 = 1 2 × x × x

[Substitute.]

Step: 5

[Simplify.]

Step: 6

[Take square roots on Both sides.]

Step: 7

Hypotenuse = x 2 = 42 in.

[Step2 and step6.]

Correct Answer is : 42 in.

Step: 1

Let x be the length of the shorter leg.

Step: 2

[30^{o}-60^{o}-90^{o}-triangle theorem.]

Step: 3

Hypotenuse = shorter leg + 43

[Given.]

Step: 4

2x = x + 43

[Substitute.]

Step: 5

[Simplify.]

Step: 6

Length of the longer leg = x 3 = 3 × 43 = 12 cm

[Step2 and step5.]

Correct Answer is : 12 cm

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