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3 years ago

Can anyone help? Would appreciate it a lot for both these questions!

Mathematics

1 answer:

NNADVOKAT [17]3 years ago

8 0

Answer:

h = √65, length of diagonal = √117

Step-by-step explanation:

1) FE = DC since △FEA congruent to △CBD. Therefore FE per say = 23-15/2 = 4. Respectively we can find height "AE" using Pythagorean theorem;

AE = √(9)^2-(4)^2 = √81-16 = √65 units

2) The diagonal of this rectangle forms two smaller triangles, each of which have legs of length 4 + 2 & 4 + 4 respectively. Use Pythagorean Theorem and determine the length of the diagonal;

Legs = 6 & 8

6^2 +9^2 = diagonal^2,

length of diagonal = √6^2 + 9^2

= √117 units

<u>diagonal = √117</u>

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4 years ago

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Alex73 [517]

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Step-by-step explanation:

Given that:

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$cos2\theta = ?$

Solution:

Let us have a look at the cosine of twice the angle in terms of tangent of the angle.

Suppose, we are given the value of $tanA$ , then the formula can be written as:

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$cos2\theta = \dfrac{1-tan^2\theta}{1+tan^2\theta}\\\Rightarrow cos2\theta = \dfrac{1-(\frac{15}{4})^2}{1+(\frac{15}{4})^2}\\\Rightarrow cos2\theta = \dfrac{1-\frac{225}{16}}{1+\frac{225}{16}}\\\Rightarrow cos2\theta = \dfrac{\frac{16-225}{16}}{\frac{16+225}{16}}\\\Rightarrow cos2\theta = \bold{-\dfrac{209}{241}}$

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Therefore, the answer is:

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