A man walks off the path clambers through the garden bed to stand in the middle of a big green bush. He pulls a bicycle helmet from between the leaves and straps it on. Then he wheels a big black bike out from the bush and rides it sway.

A man walks off the path clambers through the garden bed to stand in the middle of a big green bush. He pulls a bicycle helmet from between the leaves and straps it on. Then he wheels a big black bike out from the bush and rides it sway.

A young man sits on a piece of gym equipment staring thoughtfully into space. He is completely motionless except for the fingers of one hand stroking his chin.

A young man sits on a piece of gym equipment staring thoughtfully into space. He is completely motionless except for the fingers of one hand stroking his chin.

A woman and a tiny curly-haired dog stand on the grass looking at each other. The dog has one front leg enrobed in a big white bandage. The woman has a hoodie on which are the words, “You are enough.”

A woman and a tiny curly-haired dog stand on the grass looking at each other. The dog has one front leg enrobed in a big white bandage. The woman has a hoodie on which are the words, “You are enough.”

Frozen For Tax Purposes

"ADHD label risks lifelong harm to children." If you don't label the disorder, then what we will be labelled instead is "Lazy." "Underachiever." "Doesn't live up to their potential." "Bad student." Those labels come with pain, shame, and abuse. The ADHD label comes with a chance for support.

Hi, I’m a sighted alt text user! Here are some reasons I use it: - Slow Internet on an airplane - I’m over 40, I have no idea who that celebrity is - Bluesky broke images again - My vision sucks and that text is too small to read otherwise - Conveys further context and authorial intent

Yes on a good day I can use cosec, sec and cotan and I’m always excited to do so.

Huh. That means the ratio of two sides of a triangle is the same as the ratio of the sines of the angles opposite them. I’ve never said the sine rule that way but I like it.

I kind of like this: To get from the length of hypotenuse of a right angled triangle to the length of the side opposite angle A, you multiply by sin(A). To get from the length of the side opposite B to the side opposite A in any triangle, you multiply by sin(A)/sin(B).

Yes I feel the same.

Though actually the version of the sine rule presented here is more like: Let A and B be two angles in a triangle and a and b their opposite edges. Then a sin(B)=b sin(A).

The original problem said “no sine rule” and I have to say it was nice to do it from just right-angled triangle trig. I can see why the sine rule is true here.