Answer:
10.02 meters.
Step-by-step explanation:
We have been given two right triangles. We are asked to find the value of h for our given triangles.
Using Pythagoras theorem, we will find hypotenuse of bigger triangle.
[tex]12^2+18.2^2=x^2[/tex]
[tex]144+331.24=x^2[/tex]
[tex]475.24=x^2[/tex]
[tex]x=\sqrt{475.24}[/tex]
[tex]x=21.8[/tex]
We will use area of triangle formula to solve our given problem.
[tex]\text{Area of triangle}=\frac{1}{2}\times (\text{Base*Height})[/tex]
[tex]\text{Area of triangle}=\frac{1}{2}\times (12*18.2)[/tex]
The area of the triangle would be:
[tex]\text{Area of triangle}=\frac{1}{2}\times (21.8*h)[/tex]
Upon equating both equations, we will get:
[tex]\frac{1}{2}\times (21.8*h)=\frac{1}{2}\times (12*18.2)[/tex]
[tex]10.9h=6*18.2[/tex]
[tex]\frac{10.9h}{10.9}=\frac{6*18.2}{10.9}[/tex]
[tex]h=\frac{109.2}{10.9}[/tex]
[tex]h=10.018[/tex]
Therefore, the value of h for our given triangle is 10.02 meters.
