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A sailmaker is designing a mainsail for a newly constructed sailboat. The mainsail foot is 13 feet long, the luff is 10 feet long, and the luff makes a 50° angle at the head with the leach.
Part A: Determine the length of the leach.

Part B: Find the area of the mainsail.
PLS HELP :) 50 POINTS!!!

Respuesta :

Answer:

Part A: Determine the length of the leach- 17FT

Part B: Find the area of the mainsail-64.81FT2

Step-by-step explanation:

The mainsail foot is 13 feet long, the luff is 10 feet long has the length of the leach 6.93 ft and the area of the mainsail is 64.85 [tex]\rm ft^{2}[/tex].

The mainsail foot is 13 feet long, the luff is 10 feet long, and the luff makes a 50° angle at the head with the leach, the length of the leach and the area of mainsail is requird.

What is sines law?

The law of sines refers to the ratio of side length of triangle to the sine of the opposite angle which is same for all the sides.

SinA / a = SinB/ b = SinC/c

where, the A,B,C are the angle of the triangle and a,b,c are the opposite sides of the angle of triangle.

Part A

By using the sines law,

SinA /10 = SinB / 13

SinA /10 = Sin50 / 13

A = 36.10

C = 180-(180-36.10)

C = 93.90

So, Sin36.10 / a = Sin50/ b = Sin93.90/c

Sin36.10 / 10 = Sin50/ 13 = Sin93.90/c

c = Sin93.90 × 13 ÷ Sin50

c = 16.93 ft

Part B

Area of the mainsail = 1/2 × abSinC

                                  = 1/2 × 10 × 13 × Sin93.90

                                  =  64.85 [tex]\rm ft^{2}[/tex]

Therefore, the length of the leach is 16.93 ft and the area of the mainsail is 64.85 [tex]\rm ft^{2}[/tex].

Learn more about the sines law here;

https://brainly.com/question/17289163

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