The Question:
Consider a right triangle with a side of length x opposite angle A, a side of length y opposite angle B, and a hypotenuse of length z opposite the right angle. If sinB= 1/√3 and x=4, find the length of the other side (y) and the length of the hypotenuse (z).
Explanation:
This is how I sketched the problem
right triangle diagram
It seems to me that the question has already gave us the value of y and z because sinB = opposite/hypotenuse = 1/√3 = y/z
When I enter 1 as the value for y and √3 as the value for z, I get the answer wrong.
What's the correct way to solve this problem? What am I not getting?
Best Answer
From $\sin B = \frac1{\sqrt 3} = \frac yz$ we have $z= \sqrt 3 y$.
By Pythagoreas' Theorem, we have $x^2+y^2=z^2$.
Hence:
$$16 + y^2 = (\sqrt3 y)^2 = 3y^2$$
This gives $y^2 = 8 \leadsto y = 2\sqrt 2, z = 2\sqrt 6$.