Mathematics: the hypotenuse and a side of a right angled triangle are 13cm and5cm respectively. fined the length of the third side

the hypotenuse and a side of a right angled triangle

ashleymarie11142

30.01.2022

Lenght of the third side =12

Step-by-step explanation:

$hypotenuse = 13 \\ opposite = 5 \\ adjacent = x \\ {hyp}^{2} = {opp}^{2} + {adj}^{2} \\$

${13}^{2} = {5}^{2} + {x}^{2} \\ 169 = 25 + {x}^{2} \\ 169 - 25 = {x}^{2} \\ 144 = {x}^{2}$

$\sqrt{144} = \sqrt{ {x}^{2} } \\ 12 = x$

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jwbri

02.01.2023

m<R = 137°

Step-by-step explanation:

Points to remember

Sum of opposite angles of a cyclic quadrilateral is 180°.

From the figure we can see a cyclic quadrilateral.

To find the value of y

From the figure we get angle R and angle P are opposite to each other.

m<R = 3y + 8 and m<P = y

m<R + m<P = 180

3y + 8 + y = 180

4y + 8 = 180

4y = 180 - 8 = 172

y = 172/4 = 43

To find the measure of R

m<R = 3y + 8

= 3*43 + 8

= 129 + 8 = 137

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