How do i solve a right triangle?

Question

i have a right traingle. all i know is side a=12 and angle A=26.75 degrees. how do i find side b, c, and angle B?

Answer 1

Do you remember you SIN, COS, TAN equations?
is you know one angle and one length you can figure out the other lengths by using the appropriate SIN/COS/TAN equation. i do not know which length a is nor do i know if angle A is opposite side a or one one of the ends so i can help with specifics, but lets assume that ang.A is opposite side "a" and that side "a" is NOT the hypotenuse.
We can say;
sin(26.75) = Opposite side/hypotenuese
sin(26.75) = 12/H
... now you need to lookup sin(26.75) using a calculator .. google calculator says: sin(26.75) = 0.998920815
.. so now we have:
0.998920815 = 12/H
or H = 12/0.998920815 = 120.129642107818
... now you know the length of the hypotenuese, and you can simply use a^2 +b^2 = c^2, where you were given a and you just solved for c

Answer 2

The right angle is 90°, and angle A is 26.75°. So, if you subtract 180° - 90° - 26.75°, you will get that angle B is 63.25°.

I will assume that side c is the hypotenuse. If it isn't, then this is not correct.

For the 26.75° angle, 12 is the opposite side measure, and c is the hypotenuse. The trig function that involves the opposite and hypotenuse is sine.

sine of an angle equals opposite over hypotenuse

So, sin 26.75° = 12/c

If you cross multiply, you get (sin 26.75°)c = 12
so, c = 12/sin 26.75°

c is approximately 26.66

To find b, you could do a similar process with tangent, but it would probably be easier to use the Pythagorean theorem.

26.66² = 12² + b²
710.7556 = 144 + b²
566.7556 = b²
b = sqrt(566.7556)
b = 23.81

Answer 3

It's a right triangle, so the angles have to add up to 180°. You know that one angle must be 90°, and ∠A = 26.75°. B is presented as an unknown, so assume that it is not the 90° angle.
∠C = 90°
∠B = the remaining angle = 90° - 26.75° = 63.25°

sin(26.75°) = 12/c
c = 12/sin(26.75°) = 26.67

cos(26.75°) = b/c
b = c*cos(26.75°) = 23.80

http://i233.photobucket.com/albums/ee195/DWRead/Tom-w.jpg

Answer 4

B=90-26.75=63.25
b=atanA=12*tan(26.75)
c=a/cosA=12/cos(26.75)

Answer 5

Angle B is a right angle = 90
so angle C= 180-(angle a + angle B)
= 180- ( 90+26.75)
= 180- ( 116.75)
= 63.25

Answer 6

Well, if A=26.75, B=90-26.75=63.75

Sin26.75 = 12/c
Tan26.75 = 12/b

c=12/sinA = 26.66
b=12/tanA = 23.81