SOLUTION: In triangle ABC, a=15cm, b=21cm, and m∠C=90 degree. Solve the triangle. Can someone help me with this? Thank you.

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Question 1077715: In triangle ABC, a=15cm, b=21cm, and m∠C=90 degree. Solve the triangle.
Can someone help me with this?
Thank you.
Found 4 solutions by Boreal, MathLover1, MathTherapy, Alan3354:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
This is a right triangle with legs 15 and 21. The hypotenuse or c, is sqrt (225+441)=sqrt(666)=25.81.
can use Law of Sines
25.81/sin C=25.81= a/sin A=15/sin A; sin A=15/25.81=0.5812. Take the arc sin (0.5812)=35.53 deg angle A
21/25.81=0.8136; arc sin (0.8136)=54.45 deg angle B

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

In triangle ABC, a=15cm, b=21cm, and m < C=90 degree.
use Law of Cosines:
a%5E2=b%5E2%2Bc%5E2-2bc%2Acos%28A%29
b%5E2=a%5E2%2Bc%5E2-2ac%2Acos%28B%29
c%5E2=a%5E2%2Bb%5E2-2ab%2Acos%28C%29
c%5E2=15%5E2%2B21%5E2-2%2A15%2A21%2Acos%2890%29......cos%2890%29=0
c%5E2=225%2B441-630%2A0
c%5E2=666
c=sqrt%28666%29
c=25.8cm

a%5E2=b%5E2%2Bc%5E2-2bc%2Acos%28A%29
a%5E2-b%5E2-c%5E2=-2bc%2Acos%28A%29
cos%28A%29=%28b%5E2%2Bc%5E2-a%5E2%29%2F2bc
cos%28A%29=%2821%5E2%2B%2825.8%29%5E2-15%5E2%29%2F%282%2A21%2A25.8%29
cos%28A%29=%28441%2B665.64-225%29%2F%281083.6%29
cos%28A%29=%28881.64%29%2F%281083.6%29
cos%28A%29=0.8136212624584718
A=cos%5E-1%280.8136212624584718%29
A=35.55%B0

b%5E2-a%5E2-c%5E2=-2ac%2Acos%28B%29
2ac%2Acos%28B%29=a%5E2%2Bc%5E2-b%5E2
cos%28B%29=%28a%5E2%2Bc%5E2-b%5E2%29%2F2ac
cos%28B%29=%2815%5E2%2B%2825.8%29%5E2-21%5E2%29%2F%282%2A15%2A25.8%29
cos%28B%29=%28449.64%29%2F%28774%29
cos%28B%29=0.580930232558
B=cos%5E-1%280.580930232558%29
B=54.48°

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
In triangle ABC, a=15cm, b=21cm, and m∠C=90 degree. Solve the triangle.
Can someone help me with this?
Thank you.
This is a right triangle, so for the missing side c, we get: 

To get the smaller angle (A), calculate: highlight_green%28matrix%281%2C3%2C+tan+%28A%29%2C+%22=%22%2C+15%2F21%29%29

To get ∡B, just subtract ∡A from 90o.

Why do the other people who responded make this problem look so complex?

Why would anyone want to use the law of cosines and/or the law of sines? Unless, of course, it is so requested?

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
In triangle ABC, a=15cm, b=21cm, and m∠C=90 degree. Solve the triangle.
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It's a right triangle, so c^2 = a^2 + b^2
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sin(A) = a/c
sin(B) = b/c