What is the measure of the angle in a right triangle that is adjacent to the hypotenuse and long leg if the length of the hypotenuse = 54 and the length of the short leg = 16?

Asked on by r4rob92

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jgeertz | College Teacher | (Level 1) Associate Educator

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First draw a diagram of your right triangle. The information given states that the hypotenuse length is 54 and the short leg is 16.

You are asked to find the measure of the angle opposite this short leg. Looking at your trig function definitions, you can see that

`sin theta = ` opposite/ hypotenuse

`sin theta = 16/54`

On your graphing calculator remember to use the inverse sin function (sin^-1) when finding angles.

`sin^-1 (16/54)`

`sin theta = 17.23528526 degrees`

Round if necessary to the appropriate place value.

The measure of the angle is approximately 17 degrees.




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