+129845 We need to find c...using the P Theorem, we hve
c = √(5^2 + 15^2) = √250 = 5√10
And, using the Law of Sines, we have
5√10 / sin90 = 15 / sinB
sinB * 5√10 = 15 divide both sides by 5√10
sinB = 15 / ( 5√10) = 3/√10
And using the sine inverse, we have
sin-1 (3/√10) = B = about 71.57°
+26387 Right triangle. Angle c= 90 degrees. Side A=5. Side B=15. Find angle b
$$\tan{(B)}}=\dfrac{15}{5}=3\\\\
B=\tan^{-1}{(3)}=71.5650511771\ensurement{^{\circ}}$$
I may be wrong on this sence there are already two answers. I think both are correct. Anyway here is the way I would find angle b that is easier for me to understand.
Devide 5.(side A) into 15.(side B) = 3. this is the Tangent of Angle b
Inverse Tangent 3. to Decimal Degree = 71.56505118 D.D. of Angle b
Inverse D.D. 71.56505118 to Degrees, Minutes, & Seconds = 71'33'54.18" this is the Angle you wanted
The way I prove my answer is (side B) 15. Squared = 225. plus (side A) 5. Squared =25 sum =250 find the Square root of 250 = 15.8113883 = this is the length of (side C) (Short Leg Squared Plus short Leg Squares = Sum of Hyp. must take square root of this Sum to get the Length of Hyp.)
Sine of D.D. 71.56505118 =.948683298 times 15.8112883(side C) = Side B or 15.
Tangent of D. D. 71.56505118 = 3. times 5.(side A) = 15.
If you have any two figures on a right triangle the easest way to find anything you want about the other angles or sides is use Square Root, and prove it with Sine or Tangent. For me it is (Square Root) (Sine) & (Tangent)
