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Mrac [35]
3 years ago
5

Evaluate the function requested. Write your answer as a fraction in lowest terms. Find tan A.

Mathematics
1 answer:
jasenka [17]3 years ago
3 0

For the given triangle, the tan of angle A equals C. \frac{5}{12}.

Step-by-step explanation:

Step 1; In the given triangle, the opposite side has a length of 15 units, the adjacent side has a length of 36 units while the hypotenuse of the triangle measures 39 units. To calculate the tan of angle A we divide the opposite side's length by the adjacent side's length.

cos A = \frac{oppositeside}{adjacentside}.

Step 2; The opposite side's length = 15 units,

The adjacent side's length = 36 units.

cos A = \frac{15}{36}, dividing the numerator and the denominator by 3, we get

cos A = \frac{5}{12}, which is option C.

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Use two 2-Column proofs to show that either diagonal of a rectangle will create two congruent triangles?
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<span>Given: Rectangle ABCD 
Prove: ∆ABD≅∆CBD 
Solution:
                      
           <span> Statement                                       Reason 
</span>
  ABCD is a parallelogram          Rectangles are parallelograms since the                                                          definition of a parallelogram is a quadrilateral                                                    with two pairs of parallel sides.

Segment AD = Segment BC       The opposite sides of a parallelogram are     Segment AB = Segment CD       congruent. This is a theorem about the                                                              parallelograms.

</span>∆ABD≅∆CBD                             SSS postulate: three sides of ΔABD is                                                           equal to the three sides of ∆CBD<span>


</span><span>Given: Rectangle ABCD 
Prove: ∆ABC≅∆ADC
</span>Solution:
                      
           <span> Statement                                       Reason 
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    Angle A and Angle C                 Definition of a rectangle: A quadrilateral     
        are right angles                      with four right angles.

        Angle A = Angle C                 Since both are right angles, they are                                                                  congruent

Segment AB = Segment DC       The opposite sides of a parallelogram are     Segment AD = Segment BC       congruent. This is a theorem about the                                                              parallelograms.

            ∆ABC≅∆ADC                   SAS postulate: two sides and included                                                         angle of ΔABC is congruent to the two                                                         sides and included angle of ∆CBD
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