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Hi... I've been strugling with these three problems for  a few weeks:

 

(1) Degrees are not the only units we use to measure angles. We also use radians. Just as there are \(360^\circ\) in a circle, there are \(2\pi\) radians in a circle. Compute \(\sin \frac{\pi}{6},\) where the angle\(\frac{\pi}{6}\) is in radians.

 

(2)Find the length AC, to two decimal places.

Image:
https://artofproblemsolving.com/texer/sywndnao

 

(3)Find the length BC, to two decimal places.
Image:

https://artofproblemsolving.com/texer/enqsdotw

 Nov 15, 2020
 #1
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Quick note: to get the images for (2) and (3), post these codes to get the figures. Make sure you say Render as Image in the TeXeR

 

(2)

 [asy]
unitsize(2 cm);

pair A, B, C;

A = dir(40);
B = (0,0);
C = (3,0);

draw(A--B--C--cycle);

label("$A$", A, N);
label("$B$", B, SW);
label("$C$", C, SE);
label("$3$", (A + B)/2, NW);
label("$7$", (B + C)/2, S);
label("$50^\circ$", B + (0.5,0.15));
[/asy]

 

(3)

[asy]
unitsize(1 cm);

pair A, B, C;

A = 4*dir(71);
B = (0,0);
C = (5,0);

draw(A--B--C--cycle);

label("$A$", A, N);
label("$B$", B, SW);
label("$C$", C, SE);
label("$8$", (A + C)/2, NE);
label("$61^\circ$", A + (0.2,-0.8));
label("$43^\circ$", C + (-0.8,0.3));
[/asy]

 Nov 15, 2020

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