Find the missing leg if one leg is 18 units and the hypotenuse is 30 units

Mathematics

1 answer:

irina1246 [14]4 years ago

4 0

Answer:

Step-by-step explanation:

I will assume this is a right triangle with the information given

a^2+b^2 = c^2 is the Pythagorean theorem

18^2 + b^2 = 30^2

Subtract 18^2 from each side

18^2 - 18^2+ b^2 = 30^2 -18^2

b^2 =900 -324

b^2 =576

Take the square root of each side

sqrt(b^2) = sqrt(576)

b =24

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$\large \underline{ \mathbb{QUESTION:}}$

Find the exact value of csc² 30° + cos² 45°.

$\large \underline{ \mathbb{SOLUTION:}}$

$\tt{csc^{2} \: 30^{o} \: + \: cos^{2} \: 45^{o} \: = \: 2^{2} \: + \: ( \frac{1}{ \sqrt{2} }^{2}) }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ = \: 4 \: + \: \frac{1}{2} }$

$\:\:\:\:\:\:\:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{ \red{ = \: 4 \frac{1}{2} }}}$