Step: 1

The side of the equilateral triangle is 4.8 cm.

Step: 2

Area of the equilateral triangle = (1 2 ) ×side length × side length × Sine of included angle.

[Area of triangle given SAS.]

Step: 3

= 1 2 × 4.8 × 4.8 × sin 60°

[From the figure.]

Step: 4

= 1 2 × 23.04 × 3 2 = 5.763 cm^{2}

Correct Answer is : 9.613 cm^{2}

Step: 1

The sides of the triangle are 6.3 cm, 8.4 cm and let θ be the included angle of these sides.

[Assuming θ as the included angle would help to find the area of the triangle]

Step: 2

Area of Triangle = 1 2 × Side length × Side length × sine of included angle

[Area of triangle given SAS.]

Step: 3

= (1 2 )(6.3)(8.4) sin θ = 26.46 sinθ

[Substitue to find the area]

Step: 4

sin θ has its maximum value 1, when θ = 90°.

Step: 5

The area of the given triangle is maximum when the included angle is 90°.

Step: 6

At θ = 90° the maximum value of A = 26.46 sin90° = 26.46(1) = 26.46 cm^{2}.

[Substitute the value of Sin 90° = 1]

Correct Answer is : 26.46 cm^{2}

Step: 1

Let the side of the equilateral triangle be a in. and the height be h in. as shown.

Step: 2

sin 60° = h a

[Use the sine ratio.]

Step: 3

Step: 4

[Cross - product property.]

Step: 5

The area of the equilateral triangle = (1 2 ) × side length × side length × sin 60°.

[Write the area of an equilateral triangle.]

Step: 6

= (1 2 )(a )(a ) sin 60° = (3 4 ) ( 4 h 2 3 )

[Substitute 2 h 3 for a .]

Step: 7

= h 2 3

[Simplify.]

Step: 8

[The area of the equilateral triangle is given by 9 3 in^{2}..]

Step: 9

[Simplify.]

Step: 10

[Find square root on each side.]

Correct Answer is : 3 in

Step: 1

Let the side of the equilateral triangle be a in. and the height be h in. as shown.

Step: 2

sin 60° = h a

[Use the sine ratio.]

Step: 3

Step: 4

[Cross - product property.]

Step: 5

The area of the equilateral triangle = (1 2 ) × side length × side length × sin 60°.

[Write the area of an equilateral triangle.]

Step: 6

= (1 2 )(a )(a ) sin 60° = (3 4 ) ( 4 h 2 3 )

[Substitute 2 h 3 for a .]

Step: 7

= h 2 3

[Simplify.]

Step: 8

[The area of the equilateral triangle is given by 2 5 3 in^{2}..]

Step: 9

[Simplify.]

Step: 10

[Find square root on each side.]

Correct Answer is : 5 in

Step: 1

[Use law of Sines: Sin A a = Sin B b .]

Step: 2

Sin A = 19 × Sin 50 o 14.7 )

Step: 3

Sin A ≈ 0.99012

[Simplify.]

Step: 4

Step: 5

[Triangle - Angle sum property.]

Step: 6

[Substitute and simplify.]

Step: 7

Area of triangle ABC = 1 2 × a × b × Sin C

Step: 8

= 1 2 × 19 × 14.7 × Sin 48° = 103.8

[Substitute and simplify.]

Step: 9

Therefore, the area of the triangle ABC is ' 103.8 cm^{2} '.

Correct Answer is : 103.8 cm^{2}

Step: 1

[Given]

Step: 2

Area of triangle PQR = 1 2 × p × q × Sin R

Step: 3

= 1 2 × 19 × 9 × Sin 64° = 76.846

[Substitute and simplify.]

Step: 4

Therefore, the area of the triangle PQR to three significant digits is 76.8 cm^{2}.

Correct Answer is : 76.8 cm^{2}

Step: 1

[Given]

Step: 2

Area of triangle PQR = 1 2 × p × q × Sin R

Step: 3

= 1 2 × 17 × 12 × Sin 55° = 83.55

[Substitute and simplify.]

Step: 4

Therefore, the area of the triangle PQR to three significant digits is 83.6 cm^{2}.

Correct Answer is : 83.6 cm^{2}

Step: 1

[Given]

Step: 2

Area of triangle PQR = 1 2 × q × r × Sin P

Step: 3

= 1 2 × 13 × 18 × Sin 76° = 113.524

[Substitute and simplify.]

Step: 4

Therefore, the area of the triangle PQR to four significant digits is 113.5 cm^{2}.

Correct Answer is : 113.5 cm^{2}

Step: 1

Let the side of the equilateral triangle be a cm and the height be h cm as shown.

Step: 2

Sin 60° = h a .

[Use the Sine ratio.]

Step: 3

[Substitute and simplify for a.]

Step: 4

Area of the equilateral triangle = 1 2 × a × a × Sin 60°

Step: 5

Step: 6

[The area of the equilateral triangle is given by 753 cm^{2}.]

Step: 7

[Simplify]

Step: 8

[Apply square root on both sides]

Step: 9

Therefore, the height of the equilateral triangle is 15 cm.

Correct Answer is : 15 cm

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