Answer:
h = 5
Step-by-step explanation:
The value of h can be obtained by using area of triangle formula as well as distance formula.
[tex]A(\triangle ABC) =\frac{1}{2} \times AB\times AC \\ \\ 60 = \frac{1}{2} \times \sqrt{ {( - 3 + 3)}^{2} + (9 + 6) ^{2} } \\ \times \sqrt{ {(h + 3)}^{2} + {(9 - 9)}^{2} } \\ \\ 60 \times 2= \sqrt{ {( - 0)}^{2} + (15) ^{2} } \\ \times \sqrt{ {(h + 3)}^{2} + {(0)}^{2} } \\ \\ 120= \sqrt{ 0 + (15) ^{2} } \times \sqrt{ {(h + 3)}^{2} + 0 } \\ \\ 120= \sqrt{ (15) ^{2} } \times \sqrt{ {(h + 3)}^{2} } \\ \\ 120 = 15(h + 3) \\ \\ \frac{120}{15} = h + 3 \\ \\ 8 = h + 3 \\ \\ h = 8 - 3 \\ \\ h = 5[/tex]
