Expert: Jack Cheng - 2/5/2007

Question
I am having such a hard time with these. I do not have a clue on how to do this, I am online schooled and all I have is a text book. A text book can not help me. You do not need to give me a answer just how to do these problems. maybe give me a example if you could?

1.)Find the length of an altitude of an equilateral triangle if the length of a side is 6 units.

2.) If the hypotenuse of a right triangle is 10 units and the legs are 5 and 5√3 units, what are the sin,cos,and tan of the smallest angle.

3.) If the hypotenuse of a right triangle is 10 and one leg is 5, what is the length of the other leg?   I got 8.660254038

Thank you.  

Answer
Hi Lucas,

Sorry about the delayed reply.

1) What is the angle for an equilateral triangle? You now have an angle and a side, can you find the other leg (side)? Draw a picture, it really helps.

2) Draw a picture first. Do the sides look familiar to you? ... it's 60-30 special right triangle.  But you don't need that, once you've drew the picture, you know which is the smallest angle. sin is the ratio of the side opposite the angle over the hypotenus, cos is the ratio of the side adjacent the angle over the hypotenus, and tan is the ratio of the side opposite over the side adjacent.

3) You are absolutely right... just use the Pythagorean Theorem.

~ Jack