Thread: Sketch a triangle that has acute angle θ, and find the other five trigonometric ratio

My book provides an example how to do cos alpha 3/4. I know how to do cos. But there are no examples for tangent. I'm sure pythagoras theorem will be used but i do not understand where the 4 is coming from.

If the cosine of the angle is 3/4, draw a right-angled triangle with sides 3, and hypotenuse 4. This satisfies the Pythagorean Theorem. The 4 is given in the problem, is the calculated value for the side that is not given. Now the tangent would be (opposite side/adjacent side) = /3. The sine would be the opposite side divided by the hypotenuse.

Is this what you are asking?

no, i would like to see how one goes about solving what i attached, the tangent theta = square root 15. i do not know where the four comes from. also, if a formula could be provided for how one solves the problem i attached. i only mentioned cosine 3/4 to show i understand how to do these types of problems regarding cosines.

i figured it out