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A right triangle has a hypotenuse of length 59 and one leg of length 23.

Part A: Determjne the angle measure of the other two acute angles in the triangle. Round to the nearest hundredth.

Part B: Determine the side length of the other leg.

Respuesta :

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Answer:

Part A) The measure of the other two acutes angles are [tex]=67.06\°[/tex] and [tex]22.94\°[/tex]  

Part B) The side length of the other leg is equal to [tex]54.33\ units[/tex]

Step-by-step explanation:

Part A)

see the attached figure to better understand the problem

we know that

In the right triangle ABC

[tex]cos(A)=\frac{AB}{AC}[/tex]

substitute the values

[tex]cos(A)=\frac{23}{59}[/tex]

[tex]A=arccos(\frac{23}{59})=67.06\°[/tex]

Remember that

[tex]A+C=90\°[/tex] -------> by complementary angles

[tex]C=90\°-67.06\°=22.94\°[/tex]    

Part B)

Applying the Pythagoras Theorem

[tex]CB^{2}=AC^{2}-AB^{2}[/tex]

substitute

[tex]CB^{2}=59^{2}-23^{2}[/tex]

[tex]CB^{2}=2,952[/tex]

[tex]CB=54.33\ units[/tex]

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