If the leg of a triangle is 4 and the hypotenuse is 10 what is the number of the other leg

Mathematics

1 answer:

beks73 [17]2 years ago

7 0

Answer:

$\LARGE{ \underline{\underline{ \sf{\pink{ Required\: answer:}}}}}$

Given - One leg of a triangle is 4

hypotenuse is 10

To find - Other leg

Solution -

Using Pythagoras Theorem

<h3>(Altitude)^2 + (base)^2 = (hypotenuse) ^2 </h3>

(4)^2 + (x)^2 = (10)^2

(x)^2 = (10)^2 - (4)^2

(x)^2 = 100 - 16

x^2 = 84

x= root 84

x = 2 × root 3 × 7

x = 2 root 21

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$\mathrm{Solve\:with\:the\:quadratic\:formula}\\\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\mathrm{For\:}\quad a=1,\:b=1,\:c=-7\\\\x =\frac{-1\pm \sqrt{1^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}$