Question

A right triangle has a hypotenuse of length 10 units and includes a 40° angle. What are the length of the other two size

Answer 1

`6.43,7.66`

1) Let's sketch this out to better grasp it:

2) Since the sum of the interior angles is 180º, we can write out the following to find the missing angle:

`\begin{gathered} 40+90+\alpha=180 \\ 130+\alpha=180 \\ \alpha=180-130 \\ \alpha=50 \end{gathered}`

3) We can find the lengths by using trigonometric ratios (sine, cosine, tangent).

`\begin{gathered} \sin (40)=\frac{opposite\text{ leg}}{hypotenuse}=(b)/(10) \\ \sin (40)=(b)/(10) \\ b=10\cdot\sin (40) \\ b\approx6.43 \\ \\ \sin (50)=(c)/(10) \\ c=10\cdot\sin (50) \\ c=7.66 \end{gathered}`