Answer:
For ∆1 , x = 20 , y = 10√2
For ∆2 , x = y = 11
Step-by-step explanation:
Here in the first right angled triangle one of the angles is 45°. And one of the known side is 20 . We need to find out the value of x and y.
- Since two angles are 90° and 45° , therefore the third angle will be 45° .
- And as we know that the sides opposite to equal angles are equal. Therefore ,
[tex]\rm\longrightarrow \underline{\underline{ x =20}}[/tex]
Again , we use ratio of sine to find y , as ,
[tex]\rm\longrightarrow sin45^o =\dfrac{p}{b}\\ [/tex]
[tex]\rm\longrightarrow \dfrac{1}{\sqrt2}=\dfrac{20}{y}\\ [/tex]
[tex]\rm\longrightarrow y =\dfrac{20}{\sqrt2}=\dfrac{2\times 10}{\sqrt2}\\ [/tex]
[tex]\rm\longrightarrow \underline{\underline{ y = 10\sqrt2}} [/tex]
[tex]\qquad\rule{200}2[/tex]
Again , in the second Triangle , we may use ratio of sine to find the value of y , as ;
[tex]\rm\longrightarrow sin45^o =\dfrac{p}{b}\\ [/tex]
[tex]\rm\longrightarrow \dfrac{1}{\sqrt2}=\dfrac{y}{11\sqrt2}\\ [/tex]
[tex]\rm\longrightarrow y =\dfrac{11\sqrt2}{\sqrt2}\\ [/tex]
[tex]\rm\longrightarrow \underline{\underline{ y = 11}} [/tex]
- Again , we know that the sides opposite to equal angles are equal . Therefore here ,
[tex]\rm\longrightarrow \underline{\underline{ x =11}}[/tex]
