Respuesta :

maforchrist

Answer:

469.24

Step-by-step explanation:

you have two angles and a side so you can use sine rule to get another side preferrably WY

38/sin40=WY/sin113

WY=54.4

(113 is from subtracting present angles from 180)

using an alternative formula for area which is

[tex]1 \div 2 \: a \: b \: \sin(c) [/tex]

1/2×54.4×38×sin27

(in this formula the angle has to be enclosed by both sides)
Answer

469.42~ ft^2

Explanation

The area of a triangle can be obtained using a formula

1/2absinC

Angle C being YXW is the easiest to work with for reasons revealed later (when using sine rule)

To obtain this angle:

180 - 40 - 27 = 113

Now, you have to use the Sine Rule

Side a/sin (angle A) = Side b/sin (angle B) (or inverse)

38/sin40 = side b/sin 27

Side b = 38/sin40 • sin27

Side b = 26.84~ ft

Since you now have side b and side a as well as angle C (worked out earlier, you can use the formula

1/2absinC

1/2 • 38 • 26.84 • sin(113)

= 469.42~ ft^2

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