Question

In a right triangle the length of the hypotenuse is a and the measurement of one of the

acute angle is a. Find the measurement of the other acute angle and the lengths of the
legs.

Answer 1

The measure of the acute angle = 90 - a

Leg 1 = a cos(a)

Leg 2 = a sin(a)

Explanation:

In a right triangle ,the two acute angles are complementary

We are given that the measure of one of the acute angles is ‘a’

Then

The measure of the other one is ‘90 - a’

Now, we use the law of sine to determine the length of the legs :

Let x and y be respectively the length of the two legs.

`(x)/(\sin \left( 90-a\right) ) =(a)/(\sin \left( 90\right) )`

`\Longleftrightarrow (x)/(\sin \left( 90-a\right) ) =a`

`\Longleftrightarrow x = a *\sin \left( 90-a\right)`

`\Longleftrightarrow x = a *\cos \left( a\right)`

On the other hand,

`(y)/(\sin \left( a\right) ) =(a)/(\sin \left( 90\right) )=a`

Then

`y = a * \sin(a)`