if m

Question

if m<C=90 degrees , side c=29 , and side a = 21 , then side b is?

Shadow · Answer

hello @hottpinkkiller

Shadow · Answer

$$\frac{ Sin C }{ c } = \frac{ Sin A }{ a } \rightarrow \frac{ Sin 90 }{ 29 } = \frac{ Sin A }{ 21 }$$

Using the Sin rule, we can create an algebraic equation to solve for A, the angle opposite to side a. Then by subtracting 90 and the measure of angle A, we can get the measure of Angle B and thus use that with the Sin rule to get side B.

Shadow · Answer

This is one avenue, there are others though.

Shadow · Answer

You can also use the Cosine rule after getting the Angle opposite to side b.

Narad · Answer

Apply Pythagoras' theorem
$$b=\sqrt {(c^2-a^2)}=\sqrt{29^2-21^2} =20$$

Shadow · Answer

Or that lol.

hottpinkkiller · Answer

thank yall you guys are life savers.

Shadow · Answer

Narad's solution is much easier. C being 90 degrees indicates that this is a right triangle and justifies the use of Pythagoras' Theorem, which makes this much quicker.