Question

Type the correct answer in the box. Round off your answer to the nearest integer.

B
A and Care right angles. m p =___degrees.

Answer 1

59°

Explanation:

In triangle DAB, by Pythagoras theorem:

`DB= \sqrt {6^2 +5^2} =√(36+25)=√(61)`

Next, in triangle DCB, by Pythagoras theorem:

`DB= \sqrt {(\sqrt {61} )^2 - 4^2} =√(61-16)=√(45)`

Now, by sin rule.

`( \sin \: p)/( √(45) ) = ( \sin 90 \degree)/( √(61) ) \\ \\ ( \sin \: p)/( 6.70820393) = ( 1)/( 7.81024968 ) \\ \\ \sin \: p = ( 6.70820393)/(7.81024968) \\ \\ \sin \: p = 0.858897501 \\ \\p = 59.19301883 \degree \\ \\ p \approx 59 \degree`