Question

Is it possible to have a right-angled triangle with an angle such that `sec theta =5?`. What would the angles be in the triangle?

Answer 1

Possible.

The angles in the triangle would be: `90°, 78.5° and 11.5°`

Explanation:

By definition: `sec theta = h/a`

This means that in a right-angled triangle, the ratio between the hypotenuse and the adjacent side is `5:1`

It is possible to have a triangle where the hypotenuse is `5` times longer than the adjacent side.

Another method is to use Cos.

`sec theta = 1/costheta = 5/1`

`:. 1/sec theta =cos theta = 1/5 = 0.2`

`cos theta` is only defined for values from `-1 " to " +1`

`theta = 78.5°`