In △XYZ , XZ=11 , YZ=8 , and m∠Z=31∘ . What is the area of the triangle? Enter your answer, rounded to the nearest t

Question

In △XYZ , XZ=11 , YZ=8 , and m∠Z=31∘ .

What is the area of the triangle?

Enter your answer, rounded to the nearest tenth of a square unit, in the box.

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Hadley 4 weeks 2021-09-26T06:24:24+00:00 1 Answer 0

Answers ( )

    0
    2021-09-26T06:26:21+00:00

    Answer:

    The area of the triangle is 22.7 units²

    Step-by-step explanation:

    We can use trigonometry to find the area of an triangle if we have the length of two sides and the measure of the included angle between them, using the rule A = \frac{1}{2} (a)(b)(sin C), where

    • a , b are two sides in the triangle
    • C is the angle between the sides a and b

    In Δ XYZ

    ∵ XZ = 11 units

    ∵ YZ = 8 units

    ∵ The angle between XZ and YZ is ∠Z

    ∵ m∠Z = 31°

    – We can use the formula of the area above

    ∴ A =  \frac{1}{2} (11)(8)(sin 31)

    ∴ A = 44 sin 31

    ∴ A = 22.6616753

    – Round it the the nearest tenth

    ∴ A = 22.7 units²

    The area of the triangle is 22.7 units²

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45:7+7-4:2-5:5*4+35:2 =? ( )