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EastWind [94]
3 years ago
7

you are making a picture frame in your shop class. two peices of wood are cut to form complementary angles so they fit fit toget

her properly. one angle needs to be (2x+39) and the othwr angle needs to be (7x-21)
Mathematics
1 answer:
Andrews [41]3 years ago
5 0

Two angles are complementary when their sum is equal to 90°.

So, ( 2x + 39 ) + ( 7x - 21 ) = 90°

9x + 18° = 90°

x = 8°

Putting value of x in the angles given :

( 2x + 39 )° = 2(8°) + 39° = 55°.

( 7x - 21 )° = 7(8°) - 21° = 35°.

Therefore, the angles are 55° and 35°.

Hence, this is the required solution.

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Answer:

Step-by-step explanation:

1. a). Hypotenuse² = (Leg 1)² + (Leg 2)²

       h² = 10² + 24²

       h = √676

       h = 26

 (b). Hypotenuse² = (Leg 1)² + (Leg 2)²

       (25)² = (15)² + (leg 2)²

       Leg 2 = √(625 - 225)

                 = √400

                 = 20

  (c). Hypotenuse² = (Leg 1)² + (Leg 2)²

        h² = 4² + 6²

        h = √(16 + 36)

        h = √52

        h = 2√13

  (d). Hypotenuse² = (Leg 1)² + (Leg 2)²

        (14)² = (Leg 1)² + 7²

         Leg 1 = √(196 - 49)

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2). Hypotenuse² = (Leg 1)² + (Leg 2)²

    Leg 1 = leg 2 = 7 units [Since, triangle is an isosceles triangle]

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    Option (1) is the correct option.

3). Hypotenuse² = (Leg 1)² + (Leg 2)²

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    Area of a right triangle = \frac{1}{2}(\text{Leg 1})(\text{Leg 2})

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                                           = 120 square units

     Option (3) is the correct option.

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