One leg of a triangle is 10 inches, and the hypotenuse is 12 what is the tangent of the triangles second smallest interior angle ?

Step-by-step explanation:

One leg of a triangle is 10  inches.

Hypotenuse is 12 inches.

To find the other leg, we apply the Pythagorean formula:

a² + b² = c² (Where a and b are the legs of a triangle and c is the hypotenuse)

So if we need to find the length of the other leg of our triangle, we do this;

a² = c² - b²

a² = 12² - 10² = 44

a = (the length of the shortest leg)

The shortest angle of this right-triangle is opposite to the shortest leg.

To find the tangent of this shortest angle, we divide;

Tan angle = opposite ÷ adjacent = ÷ 10 = (in surd form)

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

the answer is d

step-by-step explanation: