Question

Please solve this for me​

Answer 1

Answer:

• The angle between AP and the rectangular base ABCD is 16.67 degrees

Step-by-step explanation:

Let us find AC first by using the Pythagoras theorem,

In right angled triangle ABC ,

$\rightarrow\mathtt{AC^{2} =AB^{2} +BC^{2} }$

$\rightarrow\mathtt{AC^{2} =(12)^{2} +(6)^{2} }$

$\rightarrow\mathtt{AC^{2} =144+36 }$

$\rightarrow\mathtt{AC =\sqrt{180} }$

$\rightarrow\mathtt{AC =13.4 cm }$

______________________

Now that we have the value of AC let us find the value of AP again by using Pythagoras theorem,

In right angled triangle ACP ,

$\rightarrow\mathtt{AP^{2} =AC^{2} +CP^{2} }$

$\rightarrow\mathtt{AC^{2} =(13.4)^{2} +(4)^{2} }$

$\rightarrow\mathtt{AC^{2} =179.56+16 }$

$\rightarrow\mathtt{AC^{2} =195.56 }$

$\rightarrow\mathtt{AC =13.9 cm }$

_______________________

we know that ,

$\rightarrow\mathtt{sin\: \theta =\dfrac{PC}{AP}}$

$\rightarrow\mathtt{sin\: \theta =\dfrac{4}{13.9}}$

$\rightarrow\mathtt{sin\: \theta =0.287}$

$\rightarrow\mathtt{ \theta =sin (0.287)^{-1}}$

$\rightarrow\mathtt{ \theta =16.67}$

Answer 2

Answer:

The angle between AP and the rectangular base ABCD is 16.67 degrees

Step-by-step explanation:

Let us find AC first by using the Pythagoras theorem,

In right angled triangle ABC ,

$\rightarrow\mathtt{AC^{2} =AB^{2} +BC^{2} }$

$\rightarrow\mathtt{AC^{2} =(12)^{2} +(6)^{2} }$

$\rightarrow\mathtt{AC^{2} =144+36 }$

$\rightarrow\mathtt{AC =\sqrt{180} }$

$\rightarrow\mathtt{AC =13.4 cm }$

______________________

Now that we have the value of AC let us find the value of AP again by using Pythagoras theorem,

In right angled triangle ACP ,

$\rightarrow\mathtt{AP^{2} =AC^{2} +CP^{2} }$

$\rightarrow\mathtt{AC^{2} =(13.4)^{2} +(4)^{2} }$

$\rightarrow\mathtt{AC^{2} =179.56+16 }$

$\rightarrow\mathtt{AC^{2} =195.56 }$

$\rightarrow\mathtt{AC =13.9 cm }$

_______________________

we know that ,

$\rightarrow\mathtt{sin\: \theta =\dfrac{PC}{AP}}$

$\rightarrow\mathtt{sin\: \theta =\dfrac{4}{13.9}}$

$\rightarrow\mathtt{sin\: \theta =0.287}$

$\rightarrow\mathtt{ \theta =sin (0.287)^{-1}}$

$\rightarrow\mathtt{ \theta =16.67}$