Question 1007444


 In a right triangle, a bisector of the right angle divides the hypotenuse in the ratio of 3:5. Determine the measure of the acute angles. 

let  the acute angles be {{{alpha}}} and {{{beta}}}

if a bisector of the right angle divides the hypotenuse in the ratio of {{{3:5}}}, then the measures of acute angles be {{{alpha}}} and {{{beta}}}  will be in same ratio; so,

{{{alpha/beta=3/5}}}

{{{alpha=(3/5)beta}}}

since {{{alpha+beta=90}}}, we have

{{{(3/5)beta+beta=90}}}

{{{(3/5)beta+(5/5)beta=90}}}

{{{(8/5)beta=90}}}
{{{beta=90/(8/5)}}}
{{{beta=450/8}}}
{{{highlight(beta=56.25)}}}

now find {{{alpha}}}
{{{alpha=(3/5)beta}}}
{{{alpha=(3*56.25)/5}}}
{{{alpha=3*11.25}}}
{{{highlight(alpha=33.75)}}}