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3 years ago

in a 30-60-90 triangle, the hyptenuse has a length of 10. how long is the shorter leg (across from the 30 degree angle)?

Mathematics

1 answer:

larisa [96]3 years ago

6 0

Answer:

5 units

Step-by-step explanation:

in a 30-60-90 triangle, the hypotenuse is 2 times the value of the shorter leg. So, if the hypotenuse is 10, then the shorter leg will be 5 units because 10 ÷ 2 is 5.

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Find the value of b. Express the answer as a simplified radical.

Mama L [17]

Here three sides of a right angled triangle given.

The three sides are b, 8 and 14.

The side with length 14 is the hypotenuse here. We have to find the side of length b.

To get b, we will use Pythagoras theorem here.

By using Pythagoras theorem we can write,

$c^2=a^2+b^2$ , where c is the hypotenuse.

So here we can write,

$14^2=8^2+b^2$

$196 = 8^2+b^2$

$196=64+b^2$

To solve it for b, now we have to move 64 to the left side by subtracting it from both sides.

$196-64 = 64+b^2-64$

$196-64 = b^2$

$132=b^2$

Now to find b, we have to take square root to both sides. We will get,

$\sqrt{132}= \sqrt{b^2}$

$\sqrt{132} =b$

$b= \sqrt{(4)(33)}$

$b= (\sqrt{4})(\sqrt{33})$

$b= 2\sqrt{33}$

We have got the required answer for the side b.

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lozanna [386]

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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