# Right triangle ABC CH is altitude and AH=2, BH=8. Find the tan angle CBA

Josie Kennedy 2022-11-20 Answered
Finding tangent for angle of right triangle
Given : Right $\mathrm{△}ABC$ CH is altitude and $AH=2$, $BH=8$. Here is drawing

Find the $tan\mathrm{\angle }CBA$
Here is how I solved the exercise: From that fact that ABC is right triangle $⇒A{C}^{2}=AH\cdot AB$ (Altitude on hypotenuse theorem) \Rightarrow AC=\sqrt{2 \cdot 10}=\sqrt{20} and $tan\mathrm{\angle }CBA=\frac{AC}{AB}=\frac{2\ast \sqrt{5}}{10}=\frac{\sqrt{5}}{5}$.
However the answer in test is 12. I can't find my mistake.
You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

postotnojeyf
CW answer to remove it from unanswered queue:
For $\left(x,y,z\right)=\left(1.1,1.01,1.001\right)$, the expression is clearly $\simeq 0.22<\frac{3}{2}$, contradicting the inequality at hand.