# Finding a Side of a Triangle Using Basic Trig

My sister asked me for help on how to do this question, and for the life of me I couldn't figure out how to do it. When she was given this question a few days ago, she was only aware of the relationship between opposite sides, adjacent sides, and hypotenuses for sine, cosine and tangent("SOH CAH TOA"). Also note that line h and line b are perpendicular to each other, so there is a right angle where those two line segments meet. So the question is to find h, given that b=50, using no trigonometry other than Pythagoras' Theorem and the "SOH CAH TOA".

Note: For anybody unfamiliar with "SOH CAH TOA", it's just an easy way to remember that

$sin\theta $$=$$\frac{opposite}{hypotenuse}$

$cos\theta$$=$$\frac{adjacent}{hypotenuse}$

$tan\theta$$=$$\frac{opposite}{adjacent}$

• Do we know anything about a and c? Jun 4, 2013 at 23:42
• No information is given about a or c. Jun 4, 2013 at 23:53

There's a good reason that you can't figure out how to do it: assuming that no information was omitted, then there isn't enough information given. What they're asking you to do is determine the height of a(n apparently acute) triangle, given only its base. This is a ludicrous request.

• Ah, ok, so I wasn't the only one thinking that. Thanks for confirming. Jun 4, 2013 at 23:53