One leg of a right triangle is 16 and the hypotenuse is 54. What is the measure of the angle adjacent to the side.

Asked on by r4rob92

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The length of one side of the right triangle is equal to 16 and the length of the hypotenuse is equal to 54.

Let the angle adjacent the side be denoted by X.

`cos X = 16/54 = 8/27`

`X = cos^-1(8/27)`

=> `X ~~ 72.76` degrees

The measure of the angle adjacent to the side with length 16 is approximately 72.76 degrees.

vaaruni's profile pic

vaaruni | High School Teacher | (Level 1) Salutatorian

Posted on

Let us take the right angle triangle ABC , where angle B= 90 degree.

Then according to the question One leg i.e side BC=16 and the

hypotenuse AC= 54. We require to find the measure of angle ACB.

Let angle ACB = x.

Let us take cosine of the angle ACB i.e  cos(x).

We know that cosine of an angle A  i.e.  cos(A) = base/hypotenuse

Applying this we get :

cos(x) = BC/AC = 16/54 = 8/27 = 0.2963

Since  cos(x) = 0.2963

hence,  x =    72.6 degrees <---Answer

Sameera W's profile pic

Sameera W | (Level 1) eNoter

Posted on

Take ABC traingle

B is 90 degreee

AC = 54

BC= 16

Then the required angle(say x) is between AB and AC

Cos (x)= BC/AC

(x) = Cos inverse (BC/AC)

(x) = Cos inverse (0.2963)(x) =72.6 degreeSo the answer is 72.6 degree

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