Question

16 ftTo the nearest tenth, what is the height of the triangle?A. 9 feetB. 14.4 feetC. 17.5 feetD. 23 feethB7 ftС

Answer 1

In the right triangle, there is a relation between the 2 legs of the right angle and the hypotenuse (the opposite side to the right angle)

`(hypotenuse)^2=(leg1)^2+(leg2)^2`

From the given figure

∵ leg1 = 7 ft

∵ leg2 = h ft

∵ hypotenuse = 16 ft

→ Substitute them in the rule above to find h

`(16)^2=(7)^2+h^2`

∵ 16^2 = 256 and 7^2 = 49

`\therefore256=49+h^2`

→ Subtract 49 from both sides

`\begin{gathered} 256-49=49-49+h^2 \\ 207=h^2 \end{gathered}`

→ Take square root for both sides to find h

`\begin{gathered} \therefore\sqrt[]{207}=\sqrt[]{h^2} \\ 14.38749=h \end{gathered}`

→ Round it to the nearest tenth

∴ h = 14.4 feet

The answer is B