Embarrassing, but

Hi everyone. I was tutoring a student today, and we were both stumped on this question (well, I could do it, but I had to use non-right-angle trigonometry, and this was in a right-angle trigonometry test).

A person walks from school 1.2 km on a bearing of 265 degrees true to a milk bar, then walks the 800 m from the milkbar to home on a bearing of 120 degrees true. How far south of the school is home? How far west of the school is home? Hence, what is the distance between school and home?

The last part is obvious, you can use Pythagoras once you have the distances south and west. But how can you get those distances using only right angle trig?

Hi Prove It. You need to note that the 265 degree bearing in the first part equates to a right-angled triangle with an acute angle of 5 degrees below the horizontal and similarly for the second part, the 120 degree bearing gives you a right-angled triangle with an acute angle of 30 degrees below the horizontal.

Hi Prove It,
Your embarrassed but I'm confused. What exactly do you mean by right angle trig ?
Are you saying that we are not allowed to say, for example, that the milk bar is $\displaystyle 1.2\cos(5^{\circ})km$ south of the school ?

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Originally Posted by BobP

Hi Prove It,
Your embarrassed but I'm confused. What exactly do you mean by right angle trig ?
Are you saying that we are not allowed to say, for example, that the milk bar is $\displaystyle 1.2\cos(5^{\circ})km$ south of the school ?

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I mean that you can only use the trigonometric ratios for right angle triangles and Pythagoras' Theorem. You can't use things like the sine and cosine rules (for non-right-angle triangles).

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Hi Prove It. You need to note that the 265 degree bearing in the first part equates to a right-angled triangle with an acute angle of 5 degrees below the horizontal and similarly for the second part, the 120 degree bearing gives you a right-angled triangle with an acute angle of 30 degrees below the horizontal.

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Thanks for your response. That's actually what I did, but still couldn't get enough information.

Thanks for your responses, I now understand. :)