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Genrish500 [490]
2 years ago
7

Find m∠D. Put the answer below. m∠D =

Mathematics
2 answers:
arsen [322]2 years ago
6 0

Answer:

your answer is ‹b ok this is your answer

lana66690 [7]2 years ago
4 0

Answer:

<h2><u>m∠D = 60°</u></h2>

Step-by-step explanation:

Use the CAH from SOHCAHTOA.

CAH is cosΘ = \frac{Adjacent}{Hypotenuse}

Substitute the given values into the above formula.

The adjacent side of ∠D measures 8, and the hypotenuse (the longest side of the right triangle) measures 16.

cosΘ = \frac{Adjacent}{Hypotenuse}

cos D = \frac{8}{16}

D = cos^{-1}(\frac{1}{2})

D = 60°

Therefore, the m∠D = 60°

<em>I hope this helps!</em>

<em>I would really appreciate it if you would please mark me brainliest!</em>

<em>Have a blessed day!</em>

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The hypotenuse of a right triangle is 37 units long. Find the other two sides if the perimeter of the triangle is 84 units. Sepa
taurus [48]

Answer:

The lengths of the legs are 12 and 35 units

Step-by-step explanation:

Let c represent the hypotenuse and a and b represent the legs.  Then the Pythagorean Theorem requires that a^2 + b^2 = c^2 = 37^2 = Hypotenuse^2

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Then a^2 + b^2 = 37^2 becomes (47 - b)^2 + b^2 = 37^2, or 1369.  Therefore:

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Simplifying by combining like terms, we get:  

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Reducing all terms by division by 2, we get:

420 - 47b + b^2 = 0.  Here the coefficients are a = 1, b = -47 and c = 420.

The discriminant is therefore b^2 - 4ac, or 529, whose square root is ± 23.

Then the b values of this quadratic in b are

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b = -------------- , so that b is either 35 or 12

             2

and then side a has length a = 47 - b = 12  or  35.

Thus, a = 12 and b = 35, and c is given:  37.

Check:  Is 12^2 + 35^2 = 37^2 true?  Is 144 + 1225 = 1369?  YES

The lengths of the legs are 12 and 35 units.

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