Question

What is the length of the altitude drawn to the hypotenuse? The figure is not drawn to scale.

a)
`√(70)`
b) 70
c)
`√(19)`
d) 19

Answer 1

The correct option is A) 70

Explanation:

Answer 2

we know that
in triangle ABC
cos (alfa)=H/(14+5)--------> cos (alfa)=H/(19) equation 1

in triangle BDC
cos (alfa)=14/H equation 2
1=2
H/(19)=14/H-------> H²=19*14---------> H²=266------> H=√266
H=16.31 units
cos (alfa)=14/16.31----------> cos (alfa)= 0.8584
alfa=arccos(0.8584)=30.86°

we know
triangle BDC
sin(alfa)=h/H---------> h=sin(alfa)*H
h=sin(30.86)*16.31----------> H=8.37 units---------> √70 units

the answer is the option A) √70