The length of a shadow of a building is 26 m. The distance from the top of the building to the tip of the shadow is 36 m. Find the height of the building. If necessary, round your answer to the nearest tenth.
We can solve this problem using similar triangles. Let the height of the building be $h$.
[asy]
pair A, B, C, D;
A = (0,0);
B = (36, 0);
C = (36, 26);
D = (0, h);
draw(A--B--C--D--cycle);
draw(rightanglemark(B, C, D, 60));
label("$h$",(12,13),N);
label("$36$",(18,0),S);
label("$26$",(36,13),E);
[/asy]
By similar triangles, we have $\frac{h}{36} = \frac{26}{h}$.
Cross-multiplying gives $h^2 = 36\cdot 26$. Taking the square root of both sides gives $h = \sqrt{36\cdot 26}$.
Approximating, $\sqrt{36\cdot 26}=\sqrt{2^2\cdot3^2\cdot2\cdot13}\approx\sqrt{2^2\cdot2^2\cdot10\cdot10}=2\cdot 10 = \boxed{20}$.